i'm also on hostgator and use mail, and have found that the mail opens many connections and forgets to close them (hostgator imap limit 25). so when i open mail a second time, my imap connection limit is reached, god knows what'd happen if i had 8+ employees trying to use mail, it prob just wouldn't work and all my sites would be offline coz i get a "500 connection error, too many connections".....
apple could prob use the iphones gyro to guide the shuttle to the moon if they wanted, but can't get imap working...:0(
the ****? we're nearly in 2013!!!!! ***?
i contacted hostgator and spoke online with live chat, and the tech said "yes it's a known prob with mail, use thunderbird" i've been using that for a while and it's quite good but doesn't feel mac like. It does close imap connections when quiting which is great.
having said that. i've also been testing SPARROW for the last week and while i have cpanel open to check connections, it too works correctly e.g. opens and closes connections on quit.
so IMHO if you want a mac like app that feels like mail, use sparrow, looks very similar to mail, and works correctly as in doesn't leave imap open on quit. i'm gonna get the rest of my email over to this prog and keep testing. hope that helps. interestingly, it seems to open less connections even than thunderbird.
another thing i like about sparrow, is they've built in dropbox and cloudapp, so if you want to send mail with large attachments, it sends them to the cloud first and then i guess the recipient gets a link to which they download. (in theory, haven't been on the receiving end yet, so can't varify) thunderbird has a feature like this too with yousendit. mail is so behind now in terms of emailing.
switch to sparrow, or at least give it a try and let us know on here if things work out better as they did for me.
cheers