Thank you very much for this Emma.
In grades > general settings I changed this setting to yes: By default recover old grades when re-enrolling a user in a course (the default setting is No).
Moodle syncs with the user database once every hour and that has never caused any problems to my knowledge.
In the student registration office I found that they were working on the student's education processes the same day the student was unrolled from the Moodle course. Apparantly the student had two active processes, one was being made inactive and the course in question was then moved from the inactive process to the active one. I need to have a talk with them to check if they can do this differently in the future so the student is not unrolled.
Thanks,
Kristbjörg