When its not working, does it make any difference if you grab hold of the car aerial? When you grab hold of it you effectively alter the length of the aerial and therefore effect its ability to tune.
From what I can gather other things to consider are:
Is the aerial mounting loose?
Is the coaxial cable connection to the aerial pushed all the way in and secure?
Is the coaxial cable connection to the head unit pushed all the way in and secure?
The last two will require removal of the the aerial/head unit and as you say you have just bought the car it may be worth taking it back for them to look at (if possible).