Several times over the years, I have come across the problem you're describing with the Dyna S.
Most of the time, it was due to the gap between the little magnet in the rotor and the pickups themselves being too small. First, check that gap. Old Dynas with the blue PC board backplate have a smaller gap than the newer (metal) ones: check your instruction sheet for that gap.
Second, I have seen several Dynas where the cam with the magnet has too big a hole in the center, which lets the darn cam wander about on the advancer's center post and even jam the advancer. The solution to those was to get another cam from Dyna: they cooperated when the units were under warranty, sending a new one that was made properly. I have seen this 4 times.
Third, if the unit is running the 3-ohm Dyna coils and there are no series resistors with those coils, the triggers may have been overheated at some point. This makes them "leak", electrically speaking, and they will default to an overly advanced state as soon as they warm up. When cold, they will often time OK at the "F" marks, but as soon as the engine heats up the plate, they go to an advanced setting because they are never actually turning all the way OFF for spark, and trigger too soon. This cannot be adjusted out.
This last failure mode happened to mine, twice. The first time was after they were used with 3-ohm coils for a few weeks: the second time was after a very hot trip: I got the unit secondhand from the owner and it failed shortly thereafter.
If you have a current meter (many multimeters have a CURRENT input mode), set it to 10 amp mode and connect it in series with one of the Dyna triggers, right in line between the trigger and the coil. When the bike is cold, turn on the key (and RUN switch) and make sure the magnet is in front of that trigger: take the current reading. It should be very low, in the milliamps range. Then run the bike until it warms up the plate. shut off the engine, then turn the key back on, make sure the magnet is pointing at the trigger being tested, and re-measure that current. It should not change more than 10%. If you find that it has jumped to about 100 milliamps (0.1 amp), then that rigger is leaking: it is damaged. Repeat with the other trigger. That's the best non-Dyna test I can suggest: it has been a reliable way for me to diagnose the bikes that show up here with those troubles.