One would normally think a family member would be lobbying in private to convince people in this condition to step down. That may be happening. But who else is whispering in their ear telling them "you're doing find, hang in there..." Lobbyists for insurance companies and coal companies (McConnell)? Lobbyists for financial or legal interests (Feinstein)?

Maybe. Even likely.

But what I was really pushing back on is the idea that the political parties are strong enough to materially affect their decisions, such that their remaining in office reflects on the parties. I just think that's wrong. Political parties today are weaker than they've ever been, as institutions. Part of that is due to technology, and part of that is due to deliberate choices we've made to cut down the role of party organizations and leaders in controlling who gets elected. They just don't have anywhere near the power they used to have. Certainly not enough power to force out a sitting Senator. Whether Feinstein or McConnell stay or go is really outside of their control. And I'm not even sure they ever had enough power to force a Senator to retire before their term was up.

To 1pg's question, states probably don't have the Constitutional authority to recall or otherwise replace a Senator:

everycrsreport.com: PDF document

The Senate could expel a member, by a 2/3 vote. But regardless of what their colleagues think of the mental condition of Feinstein or McConnell, I imagine both are regarded fondly by their colleagues on their side of the aisle. They're probably not willing to subject them to the humiliation of an expulsion vote.