There are a few reasons that you might have your engine cut out.
If you have any error codes (found by plugging in a scan tool to the OBDII port on your car), they would help dramatically in being able to narrow down the array of possible answers to your problem. If you do have a faulty connection, which I don't think you do, then a code should show up to correspond with that.
If it is the case that there is no check engine light on your dashboard when the engine cuts out, nor are there any error codes on the scan tool, the most likely cause of your problem is a bad fuel pump. This is something that (depending on your car) most automotive computer systems are not able to pick up on. This is because most cars do not have a fuel pressure sensor to be able tell the car what the actual fuel pressure is, hence it thinks that there is nothing wrong. If you also start to notice that you experience a lack of power from your car when you are driving it just before it cuts out then this is almost certainly your problem. If this is your problem, you might also tend to find that the car will cut out more at higher speeds.
If you want to determine whether it definitely is the fuel pump or not, you can check out this video on the subject.
If not, the problem becomes much harder to find because there are no codes and it just cuts out randomly on occasion. At this point it might be a good idea to take it to a mechanic unless you do happen to have a VAG-COM or other sort of data logger system on hand to enable you to do further diagnostics in to what might be the root cause of your issue.
Background Engine Theory
A small lack of fuel being injected in to the internal combustion engine will result in a lack of power being generated in the explosion inside the cylinder. When there is little to no fuel being injected, this reduces the energy generated inside the cylinder even further to the point where there is not enough of a force being generated to be able to turn the crankshaft any longer.