Haha. I had this very same problem, and posted
a thread with the very same title (apparently in the "wrong" category). I reckon it stems from burst zoning and the inability to deal with the deaths when they come (all pretty much at the same time), which in turn makes the problem resonate with itself and become worse with each cycle.
Burst influx > synchronized deaths (population loss) > mass abandonment (further population loss) > new compensatory influx bigger than the previous once things calm down, restarting the cycle and escalating the magnitude of the problem.
I solved it by chasing people out of the city in between the spikes (maxed the taxes
). It calmed the whole thing down, so unless it comes back, it's fine now. You just need to spread those deaths out over time. I've been running close to 20 years after the last serious spike. There's some up and down, but nothing like before, and it's not escalating.
That said, I believe the game needs some safeguards against this, such as not having all the people die at the exact same age (or very nearly), and not have them all be the same age when they move in. Just distributing the parameter values a bit should prevent this sort of thing from happening.