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.