The cause of your flats, or of tube failures in general, can often be determined by a combination of the location and the appearance of the puncture/failure. Wondering if you remember the exact location and appearance of the failures at the valve. I can think of only three causes of failure right at the stem base:

• Pump misuse: I would think that tearing the valve base from pump misues would be apparent after a few incidents, but is possible. It would never be a clean cut, but rather a rough tear.
• Defective melding of the stem to the tube: Very rare, cheap tubes or not, usually obvious when they occur.
• Tube migration: If one uses valve stem nuts and the tires are not kept well inflated the tube can migrate sufficiently so that the rubber at the base of the valve is stretched until it finally fails. The failure typically is a crescent-shaped tear, ofent at the edge of a small "bubble" of stretched tube. The failure would be on the side of the valve toward the front of the bicycle. The failure typically takes quite a while to develop.

NOTE: I did not mention a rim problem because Unless the valve hole had a significant, sharp, downward facing burr it would cut into the side of the valve, not the base.
ALSO - I am not saying oine should not use the stem nuts - don't get that one started again!