Fuel pump problems! Help

I have a 93 CX bubbleback with a
b16a2 5 speed. It hasn't been
happening below 10 degree celcius
weather, but now as the warm
weather is here my car is acting up
again.. You know how the pump
primes for 3 seconds or so when you
turn the key to ON. When my engine
is cool, it starts fine but when my
engine is even just starting to get
warm 1 of 3 times if i shut it off the
pump wont come back on until the
engine has cooled. It also happened
when I put 91 octane instead of 87
like i usually do. I dont know if the
computer is confused but I would
really like to know how to fix this. It
can be a real pain sometimes.
Thanks yea also sometimes if comes
on for a split second before i start it ,
then i shut it off and do it again and
it'll come on longer then i try to start
it and sometimes I am successful
sometimes not.. Real pain