It depends, either you trust Audyssey and let it does its thing, or just turn it off. Audyssey's distance measurements could be affected by signal delays for various reasons, though for the front speakers, they should typically come close to the tape measured values.
https://audyssey.zendesk.com/entries/177817-Subwoofer-Distance
If you trust Audyssey on what it was designed to do then yes you should re-run it after every major move of your speakers, but a foot or two may not change things much except for subwoofers. For subwoofers, even a few inches could change things a lot. Room EQ systems such as Audyssey may not be for everyone as it's goal is to try and get your system to reproduce sound as intended but not to an individual's liking. Even if it achieves its goal perfectly in your room (that is impossible), you may still not prefer it hence the option to set the fronts to bypass, or turn the whole thing off completely.