Assuming the charger is correctly installed there should be a fuse on the positive feed from the charger to each of the batteries. So you will most probably have two fuses (or a block with two fuses on it) somewhere between the charger and the batteries. On my Bavaria 32 the charger is very close to the batteries so perhaps it is the same for you. The fuses should be easy to find.
It can only be:
1. blown fuse
2. loose connection at the charger or battery
3. internal fault in the charger causing the relevant output to fail. There is probably another output you could use for the service battery in that (very unlikely) situation.
Actually I had the opposite problem … my batteries were not charging properly when the engine was running. It took a very long time to stumble upon the problem … it was a loose connection at the split charging diode in the engine compartment. So now, each time I do any servicing, a tighten up the three nuts holding the thick cables onto the posts on the split charging diode.