I can't confirm that rest or fast-travel breaks RFSUGT, but a work-around (for this Event or for RFSU) would be to track the time spent and register the Event again with a variable set to (total - hour(s)/minutes passed) everytime you sleep/wait/etc.
Hours slept and waited can be obtained with QueryStat. For fast-travel there are maybe several ways, i personally use a constant Function in MenuMode with MapMarker - XMarkerHeading Refs checks and Player position check, which is returning the exact fast-travelled time in minutes.