The Enclave definitely makes use of old satellites.
On every of their field outposts there is always one or more a sat-dishes. They communicate only over short areas in the Capital Wasteland but maybe they are connected to a large country wide communication grid and therefore go over satellites all the time.
The Navarro base in F2 also had a big sat-dish.
Afterall, we dont know how large the Enclave really is and where they are all over the USA in 2277.
They have the knowledge about the old satellites, frequencies, flight paths etc. Of course many of them wont function anymore while others still work and just wait to recieve a connection.
In the end you just have to try to connect, one by one until you recieve a answer from the sat or not.
Maybe they are solar powered or have RTG batteries.
Like the "Bradley-Hercules" and "Highwater Trousers" weapons platforms.
I just wonder why these two were still armed. Maybe their respective command centers were nuked in 2077 before they could sent up the fire orders ?