Another habit I've gotten into, which is informational only (but that helps me! and may help you?), and doesn't require cooperation from anyone else:

If I'm staying at an HHonors property for more than one night, I'll start the stopwatch on my watch, or else write down the exact time, at which I start the internet connection. Then, at least I know very accurately when the 24-hour "death" is coming up, and can work to avoid doing something critical at that time (like being in the middle of an email compose or an FT post).

Then, as soon as I think the 24-hour "death" time has passed, I'll open up another window or tab, and use that (rather than a refresh of whatever I'm working in) to force the new sign-in.