I would check your Immobilzer and your Electronic Throttle Module. You need a scan tool for this. This is a pretty common problem on these vehicles. Did your battery ever go dead? I ask this because this often wipes out the Immobilzer adaption and the Electronic Throttle Module will not function, meaning the car will start and die, start and die until this is corrected. Any Check Engine Lights? If so there could be some helpful codes stored to help solve this mystery.
This is a comment to osita. Yes, this is what can happen to a VW if the battery goes dead. The Immobilzer and the Electronic Throttle need to be reset. I have done this several times for VWs whose batteries have gone dead.
this is to Osita. You can take your car to a very good VW shop that has a VAG ( the VW factory scan tool and reprogramming tool ). Have the technicans do a full system scan and reset ALL the adaptions and then recheck the status of all the systems. It should not take more than an hour of shop time ($100 or so ) As for the battery going dead, it is critical to have a really great battery in these cars. I recommend the Interstate Megatron series. Most batteries from generic parts stores are bunk.