logging in to sites after running CCleaner

This is only a trivial problem, but I think after I run CCleaner that it clears whatever I did to log on to various websites (eg, fanfiction dot net). I have XP with IE6 - tried Firefox but can't figure out how to make it work since I have such lg resolution on my screen - and run AVG, Zone Alarm, and tried Cookie Jar. But its cookies always get cleared out. I have transferred the sites in the Accepted part of CCleaner, but obviously just the cookie with the name is not enough.

Did a MG search but didn't run across exactly this problem, although looked at several discussions of cookies re: how to keep and to ditch. Is there a way to figure out what I need to do to prevent CCleaner from removing whatever keeps me logged in at certain sites?