Sometimes there's a hole in the tyre from an old puncture that's got big enough for bits of grit to get in it as the tyre touches the ground, nick the tube and then drop out.
I've had the odd tyre which has just become incredibly puncture-prone for no obvious reason too, and I suspect it's either this or, as RZ said, a tiny shard hiding out of view. If it's an elderly tyre, it may be time to move on.
Edit: can you identify where on the tyre the problem is by the location of the puncture on the tube ? if you've moved th tyre on the rim that may not work, but if all you did was take out and replace the tube it might be possible.