August 17, 2011 Update:
It seems that the CL part number has now been superseded by 1K0 919 051 DB. I don’t know what the changes are or if the change was spurred by a problem with the CL number. Info from this thread.
As the 5th generation cars begin to age in the U.S., a couple of newer problems are beginning to rise up. One really annoying problem is the low pressure fuel pump cutting out intermittently. It leads to the high pressure fuel pump starving of fuel and then the engine loses power for a few seconds. Utterly annoying and it can be dangerous if you’re traveling at a good rate of speed and happen to slow down in the far left. It can be difficult to get onto the shoulder. It tends to happen during a long drive in hot weather.
A newer updated pump (Part Number : 1K0 919 051 CL) is supposed to help with this problem. This is not located in the engine bay, unlike the high pressure fuel pump. This one sits underneath the rear seats. It is easy enough to replace and there are a few DIY’s floating around. Here’s a good one from the Golfmkv forums – In-tank fuel pump replacement
1stvwparts.com has the best price that I’ve seen so far at $180 dollars plus shipping.
Before changing the fuel pump though, you might want to check whether your thrust sensor has been updated to the latest revision. This sensor sits on the passenger side of the high pressure fuel pump. 06E906051K is the part number for the newest thrust sensor revision. If this solves your problem, you’ll have saved around 120 dollars.
06E906051K Thrust Sensor
markFive GTI 
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I’m having the same issue as you’ve described, i.e. intermittent cutting off but then the car fires back up albeit with a longer cranking. No fault codes are logged. Would you know which one of the 2 could it be, the pump or the thrust sensor? Thanks!
I have this problem now and I tried my mates fuel pump (in tank) and it did the same thing bit it does not do it in his gti I have replaced everything all sensors plus the high pressure fuel pump it sure what else I can do