Disclaimer - I don't own a convertible machine but have owned 2 different coverstitch machines.
Are you threading in the correct order? On my Janome, it didn't matter, but my Juki must have the looper threaded first.
When you finish chain or cover stitching, raise the needle/s to the highest point, raise the presser foot, pull the needle thread/s forward and cut, then pull your work away from you and cut the looper thread. This locks the threads so they don't unravel.