It sounds like you could have a pressure switch problem. It does not from your post sound like a constant one. When the furnace goes out, if you put a jumper wire across the two wires of the pressure switch it should fire right back up. If the little fan (inducer assembly) is making alot of noise or vibrating, this is going to be the more likely problem than the pressure switch.
unit does not have a pressure switch..........its natural draft
I have a similar unit (so it is over 20 yrs old). The symptoms described here are the same - cold start up OK, ignitor on and flame blowing for 5+ min. The all of a sudden, the flame stopped. The rest of the motors are all humming. The ignitors turned on a few times, but no gas, no flame. The main blower keeps running and blow cold air. The LED flashes then dump the error code of 2 flashes, which essentially tell me nothing - system lockout. Checked the pressure senor, closed upon startup, so there is vaccumn. I even tried shorting it when the flame went out, but no effect. I checked the flame sensor current at about 3.x uA, so this is normal. I checked the limit switches (both the one on the exchanger wall and the one facing the flame. Both are low ohmic. I have DMM on them looking for opens when the flame cut out. The voltage on them is clamped at 0 so they are close.
I am out of easy to check options. If the gas flow valve is faulty, why would it drops out in the middle of it? I did not check the AC voltage that are supposed to be driving the valve body, as the wiring connection is not quite clear to me.