Theres a couple of good basic ideas to check there. The first that stands out is Bigsurfer’s suggestion air is getting into the fuel system.
I had a second hand Bora 115bhp tdi for 3 months before EXACTLY the same thing. Would cut out mid flow, take loads of attempts to get going and then just start perfectly. It would then cut out and wouldnt start again. If it was on the flat, generally fine. I replaced the relay that Markrtw mentioned at the start of the 2nd page and it did nothing. Turns out it was a fuel pipe that had come loose to the fuel filter and at points was sucking in enough air to conk out. When I was cranking it and cranking it it was pushing the air through to a point fuel would be pumping enough diesel through but when there was too much demand on the engine it would suck in air again.
Its a basic check, just find the fuel filter which will be on the left if you are looking at the front of the car and check if its leaking diesel.
If its not this I doubt glow plugs would stop it running which is why I would attribute it to air/fuel mixture and a sensor rather glow plugs. A fault code reader is worth its weight in gold, somewhere like GSF (german swedish french) will sell one for around £20 which will be OBDII compatible.