I read where if you change the name to "lead" "rhythm" or "killer death ray" etc. it Keeps that name but drops in the profile. I as of yet have never changed a rig name so I can exclude that as a possible reason. I am having the same thing & opposite happen. Sometimes the name will change but the previous rig will return. I can hit the button that clears it first or drag and drop over it and it still will occasionally revert. When that happens I have found clearing performance is the only way to get it back to normal and quit popping something in there I don't want.
Similar problems are being discussed here in public forum "performance synchronization"
IMO rig manager kind of "spaces out" sometimes and looses sync. I love using it but I wish it was more dependable.
As a workaround, I've found that if I edit in RM but use save button on the device, (first looking at the KPA to make sure it reads the same as what I want to save), It hasn't failed yet.
I can't remember for sure, but I recall you are supposed to be able to jump between rigs without leaving the performance, and have all edits remain, then save the whole performance at once. Usually I possibly "oversave" and save before I switch rigs within a performance. I wish I didn't have to, but that's my fail safe until I know I can bounce around within a performance and save all at once without edits changing.