This is happening with Mail.app 6.6 on OS X 10.8.5, but has been going on for a few OS X versions.
In Mail.app, my account settings specify to delete junk mail after one day. Except it never gets deleted. I can set it to delete on quitting mail, but that still doesn't work. I have to delete everything in the junk mail folder manually. Items are placed in the Junk folder that are identified as junk, but they are never deleted automatically.
The accounts in question (I have the same issue in all of them) are POP3. I tried rebuilding the mailboxes, to no avail. None of the affected mailboxes are gmail, though I do have a gmail account I look at through Mail.app.
I asked this on the Apple discussion forums, but no answer there. can anyone here make any suggestions?
From the online Help for Mail.app:
This is exactly what I've set to anything other than never, but messages in the junk mailbox doesn't ever get automatically deleted.