I've never heard of a sport gaining Olympic status and then losing it. Has there been any rationale given as to why?
Other sports have lost its Olympic status before. Baseball I think for one. There are many reasons why a sport can be taken off the Olympic program. One of the reasons against taekwondo is that many IOC members consider taekwondo to be a haven for countries run by undesirables, and it gives those countries a chance to flaunt the spotlight at the IOC's expense sometimes. Countries like Iran, Cuba, Afghanistan, etc. A cuban taekwondo competitor kicked a referee in the head at the 2008 Olympics, and Fidel Castro declared him a national hero. Things like that.