I'm having a very similar issues, to what's being reported above, with Time Machine and AFP.
My MBP running 10.8.1 (Mountain Lion) can see the newly created AFP share. Permissions are in check and everything seems to be gravy. I start the TM backup and it backup progress starts. Ultimately, the backup will stop as AFP share, I believe disappears. (e.g. when the TM backup starts, a TM Disk will appear on the Desktop. When the TM Backup stops, the Disk disappears).
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