Left/weak hand thumb can't seem to find a home

I'm having a grip problem. My left(offhand) thumb can't seem to find and stay @ HOME - that is, any consistent position. It seems to want to "fly" off the pistol.

This isn't consistent for me. I don't have this problem with any consistency with my S&W M&P .22LR Fullsize or my Glock style-SIRT pistols. OTOH, it is definitely a factor in my shooting my S&W SD9VE. The thumb just doesn't seem to want to stay on the frame unless I really roll my wrist frame-ward. That, in turn, "pulls" the heel of my left hand off the grip....

Ideas? Suggestions? Free lottery tickets? Silly comments?
At this point, I'll welcome anything.:rolleyes:

Thumbs do nothing shooting. If your support hand grip is good/strong just let your thumb float out in space.

If you're pressing into the frame, then the thumb can pop off under recoil, especially if your hands get sweaty. Like Luke said, try to keep your thumbs neutral.