Make sure you've got the option checked to keep you logged in (if that's what you want it to do):
- logon.GIF (32.25 KiB) Viewed 9054 times
Clearing your browser cookies or cache will result in you having to re-log into the site. If you log in from multiple computers (or phones/devices), it will usually break your logon session from one device when you log in with another.
If using tapatalk, that's an entirely different application in itself - I haven't seen any issue using tapatalk and your computer web browser at the same time as of yet.