Dumb question - repeated flats

My Specialized allez sport '03 model has gotten 2 flats in the past month...
and only ridden twice in that time, due to travel.  I replaced the first
flat, road the bike 30 or so miles and put it in storage.  Checked it today,
and it was flat as a pancake.  Other tire is fine.  What am I not looking
at?  There does not appear to be damage to the tire?

Thanks,

jamie