I’m not sure when it started, maybe in Snow Leopard, but Mail developed a nasty habit of not always giving an audible notice when new email arrived. I wouldn’t know unless I spotted the indicator on the Dock icon. Quitting and restarting Mail would fix it temporarily, but before long it would again be silent. Restarting the computer would also remedy the problem, but I’m one of those people who never shut down my computers. Sleep? Yes. Shut down? No. I reboot only when necessary.
One of the members of MacGroup asked me to look into the problem because it was bugging the daylights out of him, too. After a lot of searching and possible answers, I finally found something that seems to work. Mind you, it’s not a total fix, but it works in my case.
Go to System Preferences > Energy Saver > Power and uncheck “Wake for network access.” That’s it. Now, if you need to keep that checked, you’re out of luck, but I don’t really need it on my iMac. I don’t know why one thing triggers the other, but apparently not enough people have complained to Apple, so the programmers have not bothered to work on a fix. Maybe one of these days. In the meantime, if you are seeing this problem, this is one solution. If it doesn’t work for you, or if you have a different solution, let me know.
One major caveat — you might not want to do this on a laptop. Disabling “Wake for network access” will disable Find My Mac and Back to My Mac. I don’t know about anyone else, but I’d like to be able to locate my MacBook Air if someone walks off with it.