The band should not move, since the program looks in the same exact spot for the texture every time. The most likely cause of the problem is that somehow you are using an older version of your save file (prior to getting it lined up).
When I need to line up sections of the fuselage, I make a grid on the 2 sections i need to line up. I usually make it 2 to 5 pixels spacing (depending on the part and it's location) then just count how far the two sections are offset and adjust it appropriately.