Yes, apple changed a lot of stuff in Lion and the next update of the TC firmware from 7.5 to 7.6 messed up a lot of stuff.. there are so many posts about the issues.. truly it would make you think Apple had lost the plot. The update to Mountain Lion.. did not bring the hoped for improvement.. on the contrary it seems to have exacerbated the issues.
Fact is the older firmware still works better.. I often recommend people go back to 7.5.2 if your TC is more than 1 year old.. early Gen 4 and every other version can go back.. later Gen 4 arrived with 7.6 and will not downgrade.. so kyboshes that as a fix for anyone with reasonably new TC.
You have done some good work discovering the issue is AFP.. if you check the TC log you will see a heap of messages which stare you in the face about AFP having issues.. yet Apple continue to ignore the problem.
At the moment.. the best bug fix is an electrical timer that shuts off the TC at midnight each night and powers it up again a minute later. Crude yes.. effective.. yes.. not the first time cheap end networking equipment has needed this kind of treatment. Seems we need to class the TC into that group now.
I haven't a proper network fix for you..
But note the following..
1. Upgrade installs seem to introduce a lot more wireless issues.. clean install of the OS is the way to go.. big pain in the BUTT I know but I have yet to see an OS successfully upgraded.. it just doesn't work like that.
2. Set the TC names for everything.. and I mean TC, wireless and hard disk to SMB compatible. (since SMB works.. !!) Ie Short, no spaces, pure alphanumeric.
3. I do not trust auto.. auto is someone else taking control.. so fix everything about wireless you can. That means.. different names for 2.4ghz and 5ghz so bands don't auto change. Fixed channels for the wireless.. so channels don't auto swap. Fix wireless mode even so wireless cannot swap eg N to G.
4. Use only WPA2 Personal security.. no other setting is designed for N wireless .. !! Keep passkey to relatively short.. ie more than 12 characters is seldom necessary.. pure alphanumeric. Unless you run an ICBM missle silo in your backyard or a fusion reactor.. security of wpa2 is very good.
5. If the TC is the main router in the network.. see if you can swap it to bridge mode and use another router.. I don't think this fixes it but might extend out the times between failures.
6. Set the DHCP lease time short.. I don't know why the computers seem to lose track of the TC name.. but keeping lease short .. ie 20min adds very little network traffic and might help to keep arp tables etc up to date.
As Han Solo says.. Good Luck.. your gonna need it.