No, you'd need to back up your bookmarks to somewhere outside of the Profiles folder so that they can be imported into a new Profile. Bookmarks can be backed up to a 'bookmarks.html' file for this purpose but read on...
Firefox 3.0 doesn't actually use 'bookmarks.html' for the working bookmarks file. Bookmarks found in this file are imported into file called 'places.sqlite'. Once the bookmarks have been imported into 'places.sqlite', Firefox has no further need of 'bookmarks.html. If you have 'bookmarks.html' in the Firefox 3.0 Profiles folder, it can be deleted without causing a loss of bookmarks. 'Places.sqlite' contains not only bookmarks but also browsing history.
Since the introduction of 'places.sqlite' in Firefox 3.0, the 'Backup' option should probably be chosen to keep a copy of bookmarks and history instead of using the 'Export HTML' option. Both options are found in 'Bookmarks > Organise Bookmarks'. The 'Backup' option produces a backup file called 'bookmarks(date).json'. This can be be used for importing bookmarks and history into a new Firefox 3.0 Profile.
It's best not to just delete a Profile in Windows Explorer. Firefox would create another one on opening but a better practice would be to let the 'Profile Manager' create a new additional Profile You can have as many Profiles as you like). Once the new Profile is working and customised to requirements, remove the faulty (or old) Profile using the Profile Manager. Firefox will keep better track of what's going on if you use the program to handle Profiles. Information here on how to create a new additional Profile. Creating an additional one is a good because if you find it doesn't cure a problem, it is possible to remove it and revert back to using the original Profile. Can't do that if the original Profile has been removed. The newly created additional Profile can be deleted in the Profile Manager if it proves not to cure the trouble.
Regarding the problem itself, it may be that a new Profile will cure it. It can be worth quickly creating and trying an additional Profile for test purposes for nearly any Firefox problem. Most Firefox faults originate from there.
However, one possibility is that the sites have changed and it's therefore not Firefox at fault at all. A site might stipulate that passwords are not saved for security reasons. I have a Yahoo Mail account where the password isn't remembered permanently. One of the two methods written about in the article Goku linked to in post #16 should help with that ...although if a site has disabled the saving of passwords/usernames for security reasons, it could be best to leave it like that.