Is it possible for the center image to drift from lp to lp?

I have no headphones.

Yes, the center image can move depending on how it was recorded and then mixed.  Does your system have a balance control?

onhwy61, No, I don't have a balance control. (That would be a nice feature).

I agree with onhwy61.  I think it has much to do with the mix of in phase and out of phase sound (too much out of phase info), but would add that whether or not it is an issue might well depend on your room and speaker set up. It does in mine anyway.

 For example in a recent record which was music of a centered vocalist and a small group (jazz) the vocalist was very sharply focused a foot or two left of center. (My speakers are set up triangulated about 9' apart and 10' from the listening chair with the axis of the speakers crossing just in front of my head. When I centered the image by shifting my chair to the right about 6 inches I lost a little bit of sharpness but it was still very good. When I shifted my chair another 6" (or more) to the right the voice went out of phase with no center image. When I listen to 'well recorded' music the image now shifts just slightly right but it is not as distracting nor is it particularly soft focused.

FWIW.

Is your turntable level? Is the cartridge properly aligned? Are there any issues with the pickup arm leads binding, or any issues with the pickup arm bearings? Is the stylus pristine and clean? Do you have this problem with sources other than LP?

Some details on your system might be helpful.