The problem with spy sats is they orbit too low, so the suffer from drag in the trace atmosphere. Also, moving them in their orbit is super useful. Covers more, plus confusing the opposition as to their location. But it takes too much fuel. If you refuel them, both problems solved.
They have onboard fuel for "stationkeeping"; most low orbit sats do. That is keeping them in their proper orbit and attitude in spite of drag.
I would expect a more elliptical orbit to be useful too. It would let you swing down lower over your target while keeping your satellite out of the atmosphere most of the time, and it would be even harder to track.
The trouble with using elliptical orbits to get low and close is that you're going incredibly fast at that altitude. This spells trouble both because you spend a small fraction of your time above your target, and because drag is proportional to the square of velocity, mitigating any savings there.
We do have uses for highly elliptical orbits, but they're usually used for long residency times on their high side. The Molniya orbit is a prototypical example.
Tracking is not difficult for groups of amateurs with telescopes. Considering that you are up against large foreign states with extensive radar and optical detection facilities, it is mostly a lost cause. Satellites have enormous solar panels.
Elliptical orbits still require station keeping. Elliptical orbits tend to circularize over time from the drag they experience at the closest point to the Earth.
They have onboard fuel for "stationkeeping"; most low orbit sats do. That is keeping them in their proper orbit and attitude in spite of drag.