Time has zero effect on the Loyalty/Influence stat. There are three ways to manage them and a few passive effects that come into play. One is by adding or removing provinces to/from an Estate which affects Loyalty/Influence by a 1/1.5 ratio respectively. So if the province you add raises Loyalty by 10, then it will raise Influence by 15, the opposite of course for removing the province. It also appears to scale in relation to your total development, so the larger you are, the less a single province affects the stat. Second is by events which seem to be on about a 5 year schedule (pulling this number out of my ass, it might be a 10 year schedule), not counting what I think are probably an added event choice for Theocracy/Monastic Order when you choose your heir. Third is by direct interaction with the estate which only affect the stats temporarily from 10 to 30 years depending on what sort of interaction you choose. Like you can buy 10 loyalty for ducats from the Clergy estate and the effect lasts 10 years. Or you can hire a level 3 Inquisitor at 50% maintenance and raise their influence by 10 for 30 years. Direct interactions can raise Loyalty or Influence or both, and some can lower loyalty, but NONE can lower Influence (at least in the Clergy/Nobility/Burghers).
I haven't checked the events files to compare them all, so the following may just be confirmation bias. It seems like there is a slight imbalance in the way Loyalty of the Burghers is gained in relation to the Nobility & Clergy. I've done 3 Burgher purges now (removed all their provinces) to help reset their Loyalty/Influence ratio and every time I have gotten them back up above 30 loyalty I get an event that essentially screws me over by either dropping their Loyalty by 15 and gaining Influence in the Clergy/Nobility, or losing 15 loyalty in both Clergy & Nobility but gaining 10 influence within the Burghers. It's a terrible catch-22 event and I may have gotten the bonuses slightly off but that is the gist of the choices, not to mention other things like losing army tradition/naval tradition or getting an advisor cost discount. The big issue with this, is that once their loyalty drops below 30, not only do you get a trade efficiency/development cost malus, but it raises unrest in any province they own by 10! So unless you own huge swaths of different culture lands to spread them around in, you're looking at separatist uprisings all over the place (or particularists if in your primary culture provinces). On top of that, the province also continues to suffer the 25% autonomy.
Almost forgot...the passive effects. With the Burghers for example, having a city with 30 or more development will passively increase their influence by an amount. There's another one for Hanseatic Influence (not sure what this means) which increases influence as well. Then it seems that trade income affects it, in my case, my low trade income is reducing their influence by 5, I can only assume that if I increase my trade income in relation to production/tax that it will increase their influence. Also, it seems owning a center of trade (doesn't appear to stack as I own Danzig/Stettin/Lubeck and the effect is only +5 influence) gives a passive effect as well. In regards to the Clergy, just by virtue of being a Theocracy/Monastic Order, they get 20 bonus influence over me, on top of the base of 20 influence (40 influence before taking provinces etc into account). Funnily enough, I haven't had a single problem with the Clergy trying to take over, I just adjust their province ownership if it gets too dangerously close to 80% influence and use my heir choice events to raise their loyalty whenever I need to top it off. Same thing with Nobility, even better in fact. I've had them at 100% loyalty and only a measly 45% influence for decades now and just keep pumping Mil MP from them at will with nary a sign of conflict coming from them.