Not everything follows logic.

For one thing, a lot of these hormones have more than one purpose, so they exist for other reasons and may continue to have sex drive as a side effect, if you like.

Secondly, a person might desire sexual relations as a mental or physical state, in that sex has always been enjoyable for them and perhaps has always been a valued bonding experience for them, so they might continue to perform those behaviours for other reasons than bodily need.

And I guess thirdly, in some species sex is used as a bonding behaviour, not just a reproductive behaviour (this can also be seen in how some specially habitually perform acts between same sex individuals). Although one might consider a 90 year old individual extreme, from an evolutionary point of view, she might still need to perform those bonding behaviours with an "alpha male" for as long as she is able.