I have the same problem except what happens is, when I launch Apple Mail the sound alerts work just fine but once my Mac goes to sleep and I log back in, the sound is now disabled unless I relaunch the app again. Quite annoying to have to constantly relaunch it every time my Mac goes to sleep.
Hope they fix this bug soon!
After trying many methods. I found this a temporary fix. The solution is to set a rule in Mail Preference to run an Applscripts if there is new email. This Applescript will play a notification sound of your choice:
tell application "Mail" to if (count of (every message of inbox whose read status is false)) isgreater than 0 then do shell script "afplay '/Applications/Mail.app/Contents/Resources/New Mail.aiff'"
You can change the path /Application/Mail.app/Contents/Resources/New Mail.aiff to any folder that containt an aiff file. For example: /System/Library/Sounds/Glass.aiff (in this folder you can find all the alert sounds of Mac OS)
1. Open Applescript Editor in Applications folder
2. Paste the script in after choosing your notification sound path
3. Save in ~/Library/Application Scripts/com.apple.mail (can name it New Mail in my example)
4. Now you can choose the script in Mail Rules setting
For the Mail rules setting
Open Mail Preferences then Rules then Add Rule. The setting like photo
There is also another method that also work. That is the Permissons Repair
1. Quit Mail app
2. Go to Applications folder/Utilities/Disk Ultilities
3. Select Macintosh HD then Repair Dish Permissions
Wait for a couple of minutes, open Mail and try to send yourselft an email again (remember to off the rule to see effect). This method is need to be repeated overtime so I still prefer the Applescript method.
Same problem. Lose all mail sounds after computer has been asleep for a while. Have to restart mail or sometimes restart the computer. It happens more frequently if Power Nap is selected. Have spoken to apple care for 3 weeks and the issue has been sent to the engineers but no response at all. I'm surprised there have not been more reports of this problem posted. Have Macbook Air 2012. Started after upgrade from Lion to Mountain Lion about 3 weeks ago.
Sounds can also be restored by going to activity monitor and quitting coreaudiod file. This has been reported before. All sounds that should have played will then play after coreaudiod file is forced quit. You can hear 4-5 sounds play right after each other depending on how many sounds that were supposed to play but didn't until the file was stopped.
Stopping the coreaudiod file in activity monitor did the trick. Thank you! Had noticed this even in Snow Leopard, but never bothered me enough to contact Apple about it. Annoying that the fix will have to be repeated every time, but maybe if enough people post about this, they'll issue a permanent fix.