Tack welding the nuts to the door is one way to go-if you don't care about doing some paint reworking. This would be more liable to be a really secure, permanent and non loosening method.
Another option is to use Riv-Nuts (I think they are called). This is the same STYLE of nuts that the automakrs used originally.
These are fairly readily available. They work like a Pop rivet, and are installed with a standard rivet tool, but leave a hollow threaded barrel attached to the inside of the door. There is the possibility that the nut may be able to spin in place IF the nut is improperly installed in the first place, IF the attaching screw is overtightened, or IF it rusts in place and then it will be difficult to remove the screw later, without using a carbide bit to grind the head off.