Sounds like the blower fan is the problem. Could be the FSR or the blower motor.

I'll second that - If you really mean it stops blowing completely, look at the fan speed resistor (fsr) or fan/blower itself. The rear has its own blower, BTW.

There are threads here on testing the fan without removing it.replacing it is a big job.
I'd consider the FSR first though. Very common failure and not hard to reach.

It may sound funny but you are saying that it is starting to flow hot after some time, so please do this test. When the AC is working correct the condenser in the front is hot, When you feel the hot air flow starts stop the car and open the hood, touch your hand with the condenser.

IF it is cold or hot makes diagnosing completely different. The hiss of sound you told in the first messages, I guess I heard that sound too when the system was over charged with AC refrigerant.

I wish you good luck.

Let me tell you what hubby did this morning (before reading this thread): He checked the heater/water valve as suggested and water wasn't flowing through. He tapped on it a bit and then it started flowing. He used a stick and could hear it coming through almost like a heartbeat. So it seems maybe it was stuck. Right now the valve is pumping, and everything seems to be flowing through. We'll know more after he drives it to see if it stops again like yesterday. Does that mean my heater valve needs to be replaced?

Glad you are moving in the right direction. Does sound like your valve, but give it a day or two to be sure. You want it fully closed in the summer to keep hot water out of the cabin, and then open in the winter for heat. It is normally open, so if you disconnect the wires, it will be open and you will get heat (it would be nice if it was normally closed...).

The seals do go bad and the inside parts sieze up. It is a common failure part on all BMW's it seems. Some people try to rebuild the valves - you can get a seal kit on ebay for $55.

UPDATE 8-8-15 (I bought this part and it arrived DOA, so I would not recommend it) --> However, xyz sells a Hamburg-Technic version for $100.

The dealer (depends which dealer) wants $150-$200.

Update

I ended up replacing the aux fan and my X5 feels like a freezer again! Thanks to everyone, especially upallnight, for your feedback and generous assistance.

Thanks for coming back and posting the solution to your problem.

i have a weird issue where the left center vent blows nice and cold but the right blows warm air....

Could be low on refrigerant. The correct way to determine this is to recover the old refrigerant and determine how much was recovered by weight and compare what a fully charge system should be by weight. The difference is how low the system is.