Most of the time when problems happen with applications or system services we assume the cause is to be found in how the service is configured, and tackle the problem by adjusting settings, disabling and re-enabling the service, or restarting the system in Safe Mode, among other approaches. Sometimes, however, the problem may be rooted in a third-party application on the system.
One such instance may have happened recently to a few people where Mail passwords may not have been saved, causing the program to ask for account passwords each time it connects to the server. This type of problem usually warrants a look at Mail's preferences and keychain entries, but it turns out that another factor could have been the popular tool SMARTReporter. In a recent update, SMARTReporter addressed a problem in which its e-mail notification feature caused Mail to forget passwords, so even if people had fully reset Mail and their keychains, if they then reinstalled SMARTReporter the problem would crop up again.
This is a good reminder that even if a tool is not directly related to another system or application function, that function may still be affected. Therefore, if you are experiencing problems with services not working, first check your system to see if you have any add-ons, "haxies," or utilities running and quit them even if you think they are not involved with the problem. Sometimes this means just quitting the program, but other times it's necessary to also quit or uninstall background processes that the programs use.
Many of the tools that tend to cause these problems more are notification services, general plug-ins, add-ons such as input managers and Internet plug-ins, and tools that interface with other programs such as those that provide e-mail alerts.
With the system stripped down as best you can, run it for a while to see if the problem persists. Run a general maintenance routine to fix permissions and clear caches on the system, and if the problem goes away then start up your various add-on programs one by one and test the system for the problem each time to see if it reoccurs.