This kind of issues are caused by aggressive session cache. Two times already I've saw two installations with bad session handling which causes that auth_token doesn't work so login doesn't work.
There is nothing wrong in cache sessions (or just about anything else) but the settings should be fine tuned. For Chevereto 3.7.0 I will add a detection system for this kind of issues, but at this time I recommend you you first try to shutdown any cache, rebuild, then try again.
Finally, this is just bad config. The system uses $_SESSION and problem is that those sessions are not being issued on next load, or the thing is just not saving properly. To be honest I don't know because I don't cache sessions, I believe that is a bad practice, or at least, aggressive session cache is a very bad practice.