Slipping clutch, I think if it slipped out of gear you would know.
The natural wear on your clutch plates will eventually cause this unless you occasionally do the adjustments. There are two, the throwout mechanism and the cable slack. If the clutch cable is tight with the clutch released, it may be holding the clutch partially disengaged - there is a weak spring in the clutch cover to take up slack but you should feel a definite increase in pull as the clutch lever moves in 1/2" or so. If it still slips with proper cable slack, it may be the throwout cam adjustment. If it still slips with all adjustments good, the clutch springs may be weak (not unusual if you have the original springs - they've been compressed for about 40 years). It could be worn friction plates or damage to them from anti-friction oil additives. I don't know if contaminated friction pates can be salvaged.
There's also a possibility the basket fingers have notches worn into their edges, with the plate edges locking into them and thus not able to move in to engage the clutch fully.
Once you have the adjustments good, it starts to cost money to look further. Removing the cover almost always means getting a new gasket. The springs are fairly cheap. The plates are not so cheap, and a special tool is helpful to get the clutch nut off. Notched basket fingers should be fixable with a careful bit of filing but you need to take the clutch apart to get at them.
