What are you doing as far as chain maintenance? I suppose it's possible you could be wearing them out that quick if you're not regularly cleaning and lubing them, especially if your bike's stored in a damp garage? Have you measured the chains yourself before you got them replaced?

I just measured my chain at 2500 miles and it was showing some wear, but not quite ready for replacement. After this weekend (heavy rain, then 30 miles on a dry chain), I probably will ask the LBS to replace it when I bring it in for a tuneup in a couple of weeks.

Chainrings every fourth chain is probably about right, but it's the four chains in 2700 miles that doesn't sound right. Are the teeth of your chainrings worn?

How is it that a flat costs you $5? You're not replacing the tube every time you flat, are you? Get a patch kit!

Are your brake pads at the limit of their pad material?

You should learn to check for wear yourself. Not just so you don't get taken advantage of, but so you do know to replace things before they become a hazard or a bigger problem.