THat's the problem.

I send a game as a gift to my bot, then I press on "Accept game gifts" and it says "Gifts sent to your bot will be accepted within seconds."
But then nothing, I did it yesterday and now today too, but the bot doesn't accept it.

I have cancelled and sent the game many times but nothing else happens.

Edit: I have just sent a second game as a gift, I clicked on accept game gifts, and it accepted the 2nd one, but not the one I sent yesterday.

The first one was won in the steam auction, could it be the reason? (Anyway I sent another games won in the auction winter sale in 2014 some months ago with no problems)

If the game was won in auction you can no longer send them here. Steam disabled the option to accept those game as gifts.