My commuter bike has a Sturmey Archer 5 Speed alloy hub (X-FR5) which has now started to slip out of gear regularly in gears 4 & 5. When this happens, it slips for a small part of a chainwheel revolution before taking up the drive again. If I backpedal when this happens, there is a clicking sound like a pawl in a freewheel but slower and much louder.
The lower gears 1, 2 & 3 work fine.
The adjustment of the gear shifting chain and pull rod is correct.
The operating cable is well lubricated, and as smooth in operation as it always has been.
I have also tried deliberately overadjusting it in both directions without improvement.
There are many websites with Sturmey Archer info but the X-FR5 hub is not covered in detail.
Lastly, how do you oil a SA hub which has no oil hole in it?
The same suns are used for gears 1/5 and 2/4, so the isuns/planets should be fine. It may be the internals that drive the planet cage. It suspect it is the pawls that allow the driver to drive the planet cage. Make sure they're springing back into position.