I'm still uncertain but I'd vote for the ON version - to give up sounds pretty intransitive indeed. But please remowe the following 'the': "never give up on things that make you smile".

Er... remove, of course, nothing to do with grass - I urgently need a new keyboard :)

thank you alois for your comment

It depends: if you are hoping for one of the things that makes you smile, don't give up on it, it will surely come.

If you have the things that make you smile, then you would not give them up = reliquish them