2004 mazda tribute wont start sometimes

Hi have a question regarding a
mazda tribute luxury 2004 model
(auto)

Sometimes (not always) the car won't
start. I cranks to turn over but wont
catch. The weird thing is i can try to
start it 10 times and it will do the
same thing but if i just pull the key
out and try again it starts up
everytime. It seems to mainly do this
if i've been driving, stop and try and
start the car 10mins-30mins later. I
don't think its to do with a hot start
because if i drive for abit, stop and
then start the car a few minutes later
it will start no problem. I can hear the
fuel pump come on and the fuel relay
fuse is fine. All lights come on but i
have noticed when it wont
catch(start) the antenna will auto roll
down again (like when you shut the
car off) so makes me wonder if its to
do with the anti theft system? Or
something electrical? Or something
else....car runs fine other then this.

Thanks