Sounds like you've got a problem with your setup.
This advice is one time only, you only need to clear your cookies once and then reboot firefox/ie/opera so you get a new one. I don't know why you'd have to delete cookies after a visit, if you mean you have to login each visit then a cookie isn't being saved. You need to make sure the old one is deleted (do it manually if need be), and then check that your not blocking one from being issued (check your av/firewall too). Alternatively, try click log out whilst logged in and then log back in again, i hear that sometimes works for cookie problems.
I get persistant logins for all three browsers after deleting cookies once in firefox (and I only had to do that because i login in whilst i was updating phpbb a few days back), so its a local problem from the phpbb2.0.20 update.
You will probably not have problems on a different browser / machine, if you've got tha ability to test, and you get the same problem let me know and i'll see if there's anything that can be causing it