I know very little about printers, and even less about their paper handling and duplexing technology. So everything below is a wild guess:

You could theoretically see if there's a firmware update to the printer available. Perhaps there is something in the firmware that messes up the timing of one of the actuators in the duplexer, and maybe they fixed it.

I don't know the paper path of the printer, but it's also possible that there is a faulty actuator somewhere, something that is only needed when you're feeding a page into the duplexer from tray2. The actuator works for a while on the first activation, and sometimes works for the second activation, but then always fails on the third, for example.

I'd also triple check that all the parts are well seated, for example that the duplexing assembly is fully seated and attached well to the rest of the printer. That sort of thing. I've seen duplexing assemblies fail and spew paper because they weren't quite seated into the rest of the printer.

If Tray1 and Tray2 are interchangeable, see if trading the paper trays makes the problem move to the other tray. If so, maybe just getting another tray will solve the problem.