I use one of three Stanley smoothing planes in rotation. after sharpening and setting the iron correctly, I start planing as usual, after a few minutes or so the plane iron moves to one side taking more shavings from one side than the other. After resisting the iron I tighten up the cap iron some and the problem again will move again before I finish. Any ideas I would appreciate. Thank you.
Without seeing the thing in the flesh, as it were, the first thing that springs to mind from what you describe is the union or bedding of the blade on the frog allowing the iron to shift. It should be seated and able to move as you adjust it, but sufficient friction to hold it firm during work.
Possibly there is a high-spot or deposit that allows the blade assembly to pivot when you give it a thrust forward.
Where the back section of the blade sits on the frog needs to be dead flat and even.
Look for embedded crud, marks on the blade or the frog face that may line up with the pivot point. Check the cap-iron screw head is fully recessed in its slot and able to move if needed.
Check that the frog assembly is bedded flat and in line with the throat of the plane and that there’s no overlap between the frog and the mouth casting where the blade may sit.
Are all 3 planes the same type? If so, have you tried taking the bad one and one of the good ones, and swapping the blade/cap SA? If the fault moves, then it may be an issue with eh blade rather than the other parts of the plane. But the visual inspection that YrHenSaer describes should be done first.
Just curious, does the lateral adjuster swing to one side when the blade shifts? I’m guessing it does not, because why wouldn’t you simply adjust the adjuster and get on with it?
I have a No. 3 which had a cracked frog which I’m guessing flexed under load, doing somewhat the same thing you describe. The lateral adjuster did not move appreciably when the blade shifted. I would end up eventually with the adjuster hard over to port and the blade still out of wack. Resetting the blade on the frog fixed it, till it didn’t.