Check your rim tape. See if it has started to migrate in one direction, or another, exposing the edge of a spoke hole. Even the slightest amount of edge can cause, through constant rubbing, a small tear in your tube. If this is the case, consider replacing your rim tape--possibly with wider tape.

While on the topic of rim tape, some cheaper wheel manufacturers use plastic (of some sort) as a rim strip. Over time these plastic strips harden and can form small jagged edges. Eventually these edges can wear a hole in your tube. This actually happened to my friend, who came to me with the same issue as you. I replaced his rim tape, with cloth tape, and he's been fine for months, so far.

I'm not saying this is definitively your issue. However, it is worth taking a look at.

Also, you might try putting a little air in the flat tube, then squeezing it to force the air out through the puncture, to see where the hole is. This might help you find from where the puncture is originating (something on the rim or an object embedded in your tire). From there, you should be able to take a look at either your rim or tire and figure out what the cause of your series of flats might be.

...and like the others said, learn to fix your own flats (for obvious reasons).