Hmmmm.

It's been just the opposite for me. I only use one device, an iMac with Safari, and it's been very stable for at least the last month or so. I checked the "keep me logged in" box, and I stay logged in for over a week at a time.

The few times I'm not already logged in when I visit the site (only happens when I try to access the site the 1st time after the computer was shut down), the log-in fields are already pre-filled when I go to log in again, so no keystrokes required.

Maybe trying to access the site from several different devices makes it confused?