Death is random, so once they're created, they can live for decades (one of mine lasted almost a century) or a couple of days. I recruited one general while the unit was already on the march to battle. The general was pretty decent if I recall, and won a resounding victory. The unit pursued the broken enemy, and my new general died along the way to the next province. Total distance travelled = about 1 province width (started halfway to the first, and died only half-way to the second). Probably lived a few days longer than yours. If you reload to before he died, he might survive for years or decades.
While a random factor is often a good thing, especially as a modifier to an otherwise static time period, a totally random occurrence really doesn't allow for any kind of planning. The other way to handle it is a "bell curve", which can be achieved by utilizing the sum of multiple random numbers. The odds of ALL of them being high or all low are small, so most results will be nearer to the middle, with a few stray occurrences that deviate from the norm. EU3 uses "Mean time to happen", which is a random chance calculated at regular intervals, which ON AVERAGE will tend to happen in a certain amount of time, but in practice will tend to vary widely from almost immediate to effectively "never". Using a hidden countdown timer from a starting value based on a bell curve distribution would be more realistic in most cases.
Case in point: roll a D20 die, and the 1 and the 20 are equally as likely to appear as any other number. Roll 2D10 and the 2 and 20 will only appear 1% of the time each, while the 10 and 11 will occur fairly often. The tightness of the distribution can be controlled by the number of random rolls you add together, with more rolls giving less likelihood of seeing the extreme ends. That wouldn't stop generals from dying 3 days after hiring, but the odds would be infinitesimally small.
