Valve caps are on millions of cars, atvs, motorcycles and bikes, to name a few. They don't intrude on the airtight part of the tube and if anything protect the valve from being depressed.
Look elsewhere for your flats, find out where the puncture is using water, as has been said, and match the hole with wherever it is on the tire or rim of your bike. If you are getting multiple flats in the same place find the problem and fix it, if the holes are in varied places in the tread area and you don't like flats get a liner.
Ok, just saw that last post.....could your source for tubes have a bad batch? I'm assuming you are able to pump up the new tubes with no problem so it's prolly not your pump? Sometimes there is also problems with pumps damaging the valves when they are tugged off but that is usually at the bottom of the valve.
Good luck with your flat eliminating!