Email notifications come and go, in my experience. Sometimes, it seems to me, they don't get sent; other times they're redirected into my Junk mail folder; and I'm sure sometimes they get lost or filtered in transit by some router that is too smart for its own good. I wouldn't read anything into not getting email notifications, necessarily.
The issue you're having with staying logged in is almost surely an issue with your browser. The first thing to try is to clear your cache ("Delete Browsing History" or "Clear Recent History"), being sure to delete cookies (because the one that stores your login token may have become corrupted). That will (should) result in you having to log in again. Be sure that the checkbox to keep you logged in is checked, and log back in.
If you still get logged out, then it could be a configuration setting. You may have engaged (or something might have engaged for you) a security setting that continually clears cookies. That will surely make it such that you have to log in over and over again.
It could also be a problem deeper in your browser software, perhaps a corrupted DDL. If you're using IE, try using Firefox for a while; if you're using Firefox, try using IE for a while, and see if you have the same problem.