Human Capital, use it up until it can't function anymore.

These old pols are cogs in the machine, and the opportunity cost of replacing them is too high for the ruling class. So they just keep using them until they fall apart. It's all about the value of connections, and they already paid for these.

The only thing lobbists like more than someone they already bribed and have on speed dail is someone who too old to realize they're being conned.