The Reforms of Mathias
Although the successors of Konstantinos lacked his military genius, they were not short on necessary tasks. A generation of raid and razzia across the Black Sea had left northern Anatolia in disarray; even apart from the burned estates and abandoned fields, the newly militarised village cooperatives resented paying taxes to support the regulars who had not protected them, and had the means to make their displeasure felt. What was more, they had considerable support among the senatorial class. Many great families who had lost power and influence over the last century rallied to the cause of the peasants as a convenient stick to beat the Komnenoi with. Among the Komnenoi themselves, the poorer branches also tended to support the demand for lower taxation, whether from motives of nobless oblige (and there is much evidence that this was a real force in senatorial circles), or as an intra-familial power play.
The upper ranks of the Komnenoi, the strategoi of the themes and the great officers of the court at Constantinople, were perhaps not unsympathetic to demands for reform; but they faced the stark reality that, whatever its efficiency against raids, the regular army was needed to hold the border against Croatian hill-tribes and Russian boyars. They also pointed out, with some justice, that with the conquest of the Crimea, the Cossack problem was well under control, and that the village militias had not contributed to the victory of the Ingulets.
A second thread was the unintended effects of importing half a Cossack host. Konstantinos had intended to weld together Roman discipline with Cossack light-cavalry skills to create an unstoppable force, and as long as he was in command, the combination did indeed defeat all comers. But the Cossacks could not be kept mobilised forever. Konstantinos had made provision for the military problems he foresaw with this, by ensuring that the Cossacks were given land near the base areas of powerful Roman units; but he had not foreseen how their egalitarian, all-adult-males democracy would spread and subvert the traditional patron/client relationships of Roman land-ownership.
The Komnenoi elite, then, were caught between two fires: On the one hand the peasants of Anatolia demanded lower taxes, which would cripple the army. On the other hand the peasants of the Balkans demanded local representation and restrictions on absentee landlords, which would limit the wealth (which came partly from rents, but also from patronage and influence, or in other words, exactly that corruption and abuse the villages wanted curbed) of the senatorial class, who might own as many as a hundred estates spread over multiple themes.
To point out that there was unrest and agitation, of course, is not to say that the Roman state was doomed to either reform or collapse. The army remained loyal, and the mob of Constantinople (who were, it is worth noting, the second-greatest beneficiary of the imperial Fisc, which paid for most of their grain) were not much affected by the troubles, which remained largely rural. Mathias might have turned to the army, or even to the Cossacks, and restored order by fire and sword; it is not as though the unrest ever approached the level of the Byzantine civil disorders of the early twelfth century, with half of the nominally Imperial territory in open revolt against the Dukas dynasty. Why then did he not do so?
The answer appears to be that great strength of the Roman state, the ideal-of-service of its upper classes. It is true that the senatorial class took bribes, treated the offices of the State as private property to be handed out in exchange for favours, extorted extra-legal contributions from their tenants, and demanded respect and subservience as their natural right. But they also thought of the long term, and genuinely believed in the cause of civilisation against barbarism, identified with the cause of Rome as against all other polities. Fundamentally, the Mathian Reforms came about because Mathias and his advisors thought the agitators had a point. They therefore chose to emphasize the legal forms of pressure, consisting basically of petitions that the emperor Do Something about this or that local abuse, over the extralegal forms such as villa-burnings and tax-collector sniping. (This is not to say that such acts were not punished, sometimes quite harshly; only that Constantinople decided that they were isolated acts of banditry, to be dealt with locally, rather than incidents in a countrywide rebellion, for which the army should be called in.)
The Komnenos Restoration had covered a military coup in the midst of crisis with the legal figleaf of restoring the Senate's power to elect the Emperor as first among equals. In practice this did not interfere with the dynastic principle, since the Komnenoi could rely on having a majority of the Senate seats. Similarly, the Mathian Reforms found legal cover by 'reaffirming' the right of Roman citizens to have a voice in local affairs. In reality no such right had ever existed for tenants, and small landowners had effectively lost it even before the end of the Republic. If anything, a true restoration of ancient rights should rather have made the consulships (a minor honour, not given every year and fully in the Emperor's gift) elective and given the mob of Constantinople (or at a minimum, the Senate) the right to declare war and peace. Instead, Mathias regularised the forms of tenantry all across the empire, gave villages the right of veto over stewards of their landlord, and required stewards to live in the villages they ostensibly managed - absentee stewards being a much-reviled abuse. Further, he cracked down on bribes and nepotism in the civil service, for example by requiring bureaucrats (and clergy) to demonstrate basic literacy, and by instituting harsh penalties for obvious incompetence. Finally, he secured the consent of the great families (including of course the Komnenoi) who had profited from corruption by having the Senate meet rubber-stamp his decrees. Since this was the first time in several hundred years that the Senate had met for a purpose other than electing a new Emperor, this was considered a notable concession, even if purely ceremonial - the Senate was summoned to "advise and consent", not to deliberate or to decree. The senatorial class were mollified all the same by the consideration shown to their dignity; and, as noted, many of them supported the reforms in the first place.
Notably absent from the Mathian Reforms is any mention whatsoever of lightening the tax burden. A common joke at the time has one of Mathias's advisors pointing out that he was spending ducats by the tens of thousands on fortresses, roads, and soldiers, and not a penny on the poor; to which Mathias replies, "That's right. When the revolution comes, I'll be ready." Jokes aside, on this point the Komnenoi were utterly inflexible: The taxes that paid for the army would not be compromised whatsoever. Justice for tenants and smallholders was one thing; weakening the legions that held back barbarism, quite another. Indeed, the real tax level was actually increased, since the cessation of the Cossack raids made it unnecessary to forgive the taxes of devastated Anatolian estates - a common expedient for relief during the 1290s. However, walled or fortified villages, castellae, were permitted to pay their taxes in kind, by equipping one heavy-infantry soldier for every ten households. Again, heavy-infantry gear being very expensive (especially since most of it was produced by the State-owned forges of Constantinople), this was probably a net increase in taxes for most peasants. But serving in the army was a point of pride for many Anatolians, and equipping one's own sons for war did not engender the same feeling of resentment as sending off grain to be eaten by strangers, even if it was actually a greater slice of the household budget. Mathias thus gained heavy infantry who had trained with village militias from an early age, and who were often actually better equipped than the mandated minimums; and he did so at no cost in goodwill, even with a small gain. Although not a military genius of the calibre of Konstaninos, then, he well deserves his reputation and epithet of Mathias the Lawgiver.
Note: To have an ingame effect of this AAR development, I'm switching to Popular Law. This has the nice side effect of switching my Clergy light infantry to light cavalry, reflecting the addition of the Cossacks to the Roman army.