Only playing sinlge player games so only against AI.
So I've to play multiplayer games against real players to gain real favor points/items?
Well, can you clarify further? Are you playing in just the single player mode (eg you aren't hosting games online just against ai's, right)?
If all you are doing is single player (eg in skirmish or tournament - NOT IN MULTIPLAYER), then you should be able to accumulate favor points. If you are really just playing in single player and having this issue, here's what should fix you. Close Demigod. Search for and delete game.prefs. For me its located here: C:\Users\YOUR USER NAME HERE\Documents\My Games\Gas Powered Games\Demigod. That should likely sort you, but again, only if you are having an issue with single player in skirmish or tournament mode.
If you are playing in MP against only ai, you won't receive any favor points. However, you can still earn some favor points by unlocking achievements against the AI online (for instance, if you get to level 20 with a demigod - HINT - you can host a game online, set the starting level to 20, and you'll get some favor points for unlocking that achievement). It can be confusing as the end game results show you receiving favor, but if its against AI only, no favor will be credited to your account outside of completed achievements. And again, this is only for MULTIPLAYER.
Hope that helps you. If you have any more issues or questions, feel free to ask.