Unfortunately any time that X-Plane does the "loading flight" screen it resets the livery to whatever you selected on the initial flight configuration. You could consider reporting that as a bug to LR. *shrug*
I would sometimes do this so I wrote a script to maintain the time at which I paused the sim when resuming. https://github.com/pilsnerish/FlyWithLua-Scripts/blob/main/PauseResume.lua