Have you checked the Energy tab in Activity Monitor? There should be a column there for Preventing Sleep; if not make sure it is ticked in View > Columns in the menus for Activity Monitor.
Anything that says 'Yes', is going to be a problem and you should be starting with quitting those apps/processes.
That said, you should not be needing regularly to Force Quit applications, especially something like Mail.
An ordinary Quit (from the application menu or Command-Q) should suffice to close down apps properly. If not, and you are having to force quit apps, then you may have some other problems that need addressing.