Sachs clutches are a challenge always, theyre tiny!
Luckily the common issues are wellestablished and solvable.
1) the clutch nut. they tend to back off because for whatever dumb reason the clutch has no taper, it's only held on by the nut's torque, so hard stops can back the nut off. I've had several sachs where people gave up because sachs clutches are "impossible" only to find the nut was just loose. 10 minutes later it was running fine.
If it's a consistent issue, replace the nut with 2 thinner nuts jammed together and it'll prevent it from backing off again.
Another issue is glazed pads. this is what happens when other minor issues go ignored, the pads get hot, slip, and glaze - then they slip too much. You just pull al lthe pads and plates out and scuff them up and reinstall. easy peasy.
And finally is preload. as they wear down sometime you gotta re-shim, other things can affect it too, sometimes its wrong from prior owner doing things improperly, but theres a good video here:
Worth watching the video anyway to familiarize with the clutch.
504 can be a rather unfulfilling engine but it's a fine moped. I like sachs a lot but maybe just cuz I've spent a lot of time on em