Fighters which move faster than the target are unable to fire at it (or stick on top of it) while it's moving.
This is almost certainly the result of the fighter losing initiative.
Could you explain a bit more on this.
The fighter moves first, being faster, it faces no challenge in moving to where the target is now. Having moved, it moves no more this increment.
The target then moves far enough away from this position to prevent engagement by exceeding your weapons range is my guess.
Task groups move in ascending initiative order, so if you have a lower initiative value, then you move before they do.
So its very likely your fighter group has a smaller initiative value than that of the target, so you move, then they do.
You mentioned over
here that the targets were 5kkm/sec, so they are moving 25kkm away from your fighters every increment.
So I guess then that your weapons range is less than 25kkm, which would leave you unable to engage that target with those fighters until a commander with higher initiative is put in charge.