This "limping," as it is called, is the worst habit you can have in piano playing, and you are fortunate in having a teacher who persists in his efforts to combat it. There is only one way to rid yourself of this habit, namely, by constant attention and closest, keenest listening to your own playing. You are probably misstating it when you say that you do not "hear" it when you "limp"; it seems more likely to me that you do not listen. Hearing is a purely physical function which you cannot prevent while awake, while listening is an act of your willpower—it means to give direction to your hearing.
[14. PIANO TOUCH vs. ORGAN TOUCH]
How Organ-Playing Affects the Pianist
Is alternate organ and piano playing detrimental to the "pianistic touch"?
Inasmuch as the force of touch and its various gradations are entirely irrelevant on the organ, the pianist who plays much on the organ is more than liable to lose the delicacy of feeling for tone-production through the fingers, and this must, naturally, lessen his power of expression.
Organ-Playing and the Piano Touch
Is it true that a child beginning music lessons on an organ gets much better tone than one beginning on a piano, and does the side study of pipe-organ, after two years of extensive piano work, impair the piano touch?
It is only natural that a child can get better tone out of an organ than on a piano, because it is not the child but the organ that produces the tone. If the child's purpose, however, is to learn piano-playing it would not be wise to let him begin on an organ, because this would leave the essential element—the art of touch—entirely undeveloped. And if his piano touch has been formed it can easily be undone again by letting him play on the organ.
[15. FINGERING]
The Universal System of Marking Fingering