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

There is a great number of variables that can affect the sound in general and might cause the soundstage to shift from LP to LP. Some of these variables include but are not limited to time of day, day of week, sunspot activity, AC voltage variability, number of people in the room and changes to the system that were either forgotten or dismissed as too innocuous.

Addendum re soundstage shift

One need look no further than absolute polarity for the answer why the soundstage can shift from one LP to the next or from one track to another on the same LP. We know that inverted polarity produces an ill defined soundstage and or lack of depth, at a minimum. We also know that most if not the vast majority of audiophile recordings probably have inverted polarity. Some recordings have a mixture of correct and inverted polarity from track to track. Voila!

Another factor I forgot to mention was the recording itself, which might be found in the original master tape or could be a pressing issue.  I have tried multiple copies of the same recording and the center image is skewed one way, and when subsequently playing another recording the center image is in the middle. 

Get a preamp with a balance control!

I do not know why any home audio system would leave that out!

Recording engineers don't always put the singer centre-stage. More often than not, but not always. Sometimes they will alter the singer's volume on one channel so that they're slightly off. You can hear this on side two of Shriekback's Big Night Music: On the first song the singer is centred; on the second he is off to the right; on the final song he starts off to the left and drifts slightly towards the centre as the song progresses. I also have an album by Luke Hurley where both him and his guitar are off to the right throughout the entire album. God knows why they made that decision, but there you go.

Number 4 is, incidentally, impossible with a single close-mic which is how the vast majority of music is recorded. The only time this would happen is during an intimate live performance recorded with two extremely well placed microphones. This almost never happens.