Lifetime is tied to the TiVo Service Number, which is on a chip on the motherboard.If I'm not mistaken, lifetime is really lifetime of the motherboard or the chip on the motherboard with the proper code. As long as that works your TiVo is good.
Someone correct me if I'm wrong.
Up through the original S3, the TCD648250, it was contained in a stand-alone chip by Atmel called a crypto chip.
Someone with Surface Mount Device unsoldering and soldering experience could move it from a problem motherboard to another motherboard of the same model and as far as the TiVo servers (and the hard drive in the TiVo with the problem motherboard) know, it's the same lifetimed TiVo.
Beginning with the next Series 3 platform models, the HD (TCD652160) and the HD XL (TCD658000), the crypto chip is incorporated into the main CPU, which is a Ball Grid Array device, which means unsoldering and resoldering is a lot trickier than with SMDs, and requires much more expensive equipment, and it's probably easier to find out and fix the motherboard's problem than to move the CPU, and I'm not sure whether there's anything else on there that would tell it that it has been "monkeyed with" or not.