Your browser must be clearing all your cookies and /or cache? - that usually deletes all record of stored passwords.
the cookies for those site's & passwords are what is needed to be kept.

for IE go to internet options
on the general tab - Browsing history - go to view files -and see what kind of stuff is listed

hmm, that's all I can see to change/check - I don't use IE much anymore so hopefully someone more familiar with the settings will add some ideas.