I honestly don't know what is going on. Every time I turn off my laptop I get signed out. The biggest problem though is that whenever I try to log back in it says my password is incorrect, thus causing me to have to reset my password every time I login. I use Google Chrome, and I remember there being problems about signing up with Gmail, so maybe that's the problem.

That shouldn't be the case. Make sure that Chrome actually updates the stored password to the new one, and also activate "Roaming" when logging in to e621.