Refrigerator goes out while traveling

Is this in your 2001 5er?
Are you sure it has a pilot light?
Most rigs have an electronic spark system that actually turns the flame off and on.
If you mean the system goes into "check" status, that means the flame dies not ignite for some reason.
Most is caused by the ignitor not adjusted properly. Another cause is the metal heat shield is out of place or could be even missing.
What is make and model of refer? Has it had recalls done, if listed?

The fridge pilot light on our TT used to blow out from time to time due to gusts of wind..especially fast passing trucks. I used a piece of foil to block off the vent near the pilot light. I stuffed the foil on the inside of the door into the vent nearest to the pilot light. The remaining vents were left unblocked. Once I arrived at my destination I would remove the foil.

First make sure your pilot light is properly adjusted. The instruction manual will show the proper flame height and how to adjust it.