As long as you have a resort stay linked, your FPs will stay. Changing to another Disney resort won't affect your FPs. The only way your FPs are affected is canceling your reservation and not linking another one.
Agree with the others! We just changed our reservation, and actually ended up booking an entirely new reservation rather than modifying our original one since the availability I could see on-line was different than what the CM found while on the phone attempting to modify (and web-site woulfn't allow me to modify on-line)...Long story short I was told as long as a new Disney resort reservation is linked to your MDE account within 24h you will not lose your existing FP reservations.
Personally, I booked the new reservation on-line while on the phone with a CM. For a moment I had two packages (resort + tickets) for the same people on the same dates. Guest services was easily able to cancel the original, and move payment towards the new reservation. It took less than 15 minutes and all my FP stayed intact
....and we ended up saving >$1000 with the change. (4 nights Poly Club Level (GV) --> 4 nights Contemporary Garden Wing (GV) w/ free dining).