They don’t have “fixed” orbits because they have fuel to adjust orbits. Only just so much fuel, so their delta-vee is limited. Such an orbital change also has to be done in advance. It can’t be an abrupt change, again a finite amount of delta-vee is carried.
Any adversary with sufficient National Technical Means would be tracking the satellite and notice the orbital change.
Yeah, they have to swing it carefully and there’s a limited window when that change is useful. But they can. And do.