Although unlikely, it could be failure of the oil pump drive. I have never sen this in a spade drive pump, but I was told that if a 998 pump is fitted to a 1275, the engagement of the spade into the slot is very small and the pump spindle could fail.
With early engines with a pin-drive oil pump it was not unheard of for the pin to shear if the engine was started in extremely cold weather with thick oil.
I once thought I had the latter failure in a 970 'S', but after taking the engine out it turned out that the pump was draining down due to the manufacturing tolerances being on the limit. A new pump cured that.
When I rebuilt my 1275 S motor quite a few years back I replaced the pin drive Piper 270 cam with a star drive MD266. The old pin-drive oil pump looked to be in good condition, so it was put on the shelf as a spare.
Then about 2 years ago I was rebuilding a spare unit to 'original' spec. So I pulled the 'S' pin-drive oil pump off the shelf and to my surprise noticed that it was a 'small-bore' type pump with the shorter shaft. Luckily there must have been just enough engagement to keep the oil pump turning...