I'll get logged out 3 to 5 times a week probably on average, not counting logging in on a different computer/browser. Either from expired tokens or the forum maintenance, in total I get kicked out about 3-5 times a week.
If your IP is different than the last time you logged in, your cookie wont do you any good. You just have an IP that changes. This forum handles login cookies horribly, and it's incredibly annoying, and I can't imagine it really adds a lot of security. My IP at home is static for months, but every time I go to school, I have to login again, and every time I come home after logging in at school, I have to log in again. If you renew your IP, you'd have to log in again on the same computer.
It's not IP, it's just if you log in under any different circumstances. If you log in with one browser, even if you log in with a different browser on the same computer, it'll invalidate your cookie in the other browser.
If I log in during the a day, it's usually just once after the 2:30am - 2:40am EST period when the forum is down.
Sometimes I need to log in more, but that's rare and usually seem to happen if I have the forum up in a brower tab for a longer period of time without doing anything, just forum idling. But I'm not 100% certain about that, but that seems to be the case.
That's because this forum has horrible token handling and can't deal with expired authentication tokens in even a half-decent way.
Spend too much time editing a post? Your authentication token expires and you are sometimes logged out. Spend too much time idle? your authentication token expires and you are sometimes logged out.