If it were a tube mic, the first thing I'd suggest is replacing the tube, but....
You might try using it with a different mixer, particularly if you haven't used many large diaphragm condensers before. There could be a thermal cutoff in the mixer that temporarily cuts off phantom power if the load is too high. Odds are pretty slim, but it's worth a shot.
Also, try a different cable. If the thermal load is high enough and the cable has a cold solder joint or a partial break in the wire, the thermal expansion might be enough to significantly increase the effective resistance of the wire. (The resistance of each strand is constant, but if you reduce from 10 strands to 1 strand making contact, the total resistance goes through the roof.)
That said, with those symptoms, my guess is that the problem is probably thermal. Odds are good that there's a cold solder joint on one of the circuit boards somewhere. If you inspect the solder side of each board very carefully with a magnifying glass, you should be able to see a solder joint that is cracked, chalky, or discolored right next to the lead. Carefully touch any such joints with a low wattage soldering pencil (thus melting and reflowing the solder) and I'd expect the problem to be fixed.
If you know what you're doing, ten minutes with a $15 soldering pencil will probably fix the problem. If you aren't good at soldering, find somebody who is comfortable soldering on printed circuit boards. It's a little touchy, as you must be careful not to overheat the board or you risk the solder pads separating from the plastic, and then you're either buying a new board or trying to fix it with trace tape or silver paste, neither of which is very much fun.
(Note: this is why I specifically said a
low wattage pencil. I've gone as high as 25 watts, but I'd prefer 15.)
