Tip: If your battlestation is busy fighting one fleet, and you could fight a different battle next to it (like against another invasion fleet), the station will not be available to help. One enemy fleet attacked the station and a few patrols joined in. Another enemy fleet came from another direction and I intercepted it. Battlestation could not join despite being in range. I reloaded game to join the first fight with battlestation support, then intercept the other fleet and get battlestation backup.
@ TaLaR: Thanks, I did not think of looking for bases that way; much easier than clicking on every single star on the map. Would this work if the system their base in is unexplored? The system the base was in was explored.