This has now become irrelevant anyway as i've realised any manually learned codes are forgotten each time the battery goes flat.
I'm a bit late to this thread, but just wanted to check whether other users are seeing this behaviour - it's certainly not supposed to happen. My Amulet occasionally goes fully dead, but happily retains my Samsung TV programming without any need to relearn codes.
(I've seen one additional report of this from another new Amulet user.)
The amount of RAM used up depends on the complexity of the codes learnt, and also (to an extent) how long you hold down each button for. You should definitely see more than 13 codes - I think I verified it at about 30 codes a while ago, again using Samsung.
Something we'd like to do is add presets for the common vendors, so that no EEPROM storage is needed for most users; the total amount of space available on our IR chip is pretty limited though, so we'll need to get creative with exactly how we implement it.