I haven't had this issue with a TL-X, but I've acquired camera bodies of various types that have stuck mirrors. I doubt if there is only one way to cause it to happen, which means there isn't a universal fix either. I can only guess that it's related to the film advance not completing the full cycle, and either something has become broken, dislodged, or something is physically binding against something else. One way to find a possible cause is to remove the bottom plate and inspect the mechanics to see if they can be moved to complete the cycle -or- if they are frozen in place... and follow the connected pieces to see if there's a point of repair that's easy to access from underneath.
Most common reason for a mirror not returning is the failure of the second shutter curtain to complete its travel. Check the position of the curtain and maybe nudge it with a finger nail in the direction of travel. If that's the issue the shutter needs servicing. But, as lumiworx said, there are other possible reasons.