When the LeftAxis is not visible, the custom left axes have their labels clipped due there not being enough margin.
It looks as if the code responsible is in CalcAxisRect, part of the TCustomAxisPanel.InternalDraw procedure. This in the line:
Get(tmp).CalcRect(OldR,tmp<5); { <-- inflate only for first 5 axes }
This, I assume, would be the standard left, right, top, bottom, and depth axes. If the standard LeftAxis is not visible, then the axis label does not appear to be accounted for.

I don't want to change this code because I am afrain of what side effects there may be.
Thanks for your help and any workaround you may have.
BYOB.