I ran into the same 2.5km Range issue and found the reason why as well as the solution. The signal dies because the missile gets unloaded at 2.5km. Simply adding a keep active block solves the issue.
It's 10km for video when the transmitter and the receiver are in line of sight of eachother. Seems like Stormworks accounst signal strength based on terrain model.
I would really love it if you made a video explaining the most useful and interesting technologies and automation systems that can be added to a tank, such as an automatic anti-missile system or something similar! :-)
Have you thought of try combining the video feed and also radar? I did that Already built of my missile and it does work well by using camera feed to see where I going until the radar pickup the vehicle then it automatically take over my control to aim at it. It surprised work well and even if you aim the missile up to the sky and then dive down from above to hit the target. Oh and also I use gps on missile to me so I know where I am and it a lot higher range than video feed if the video feed cut off but the gps still show the location and the radar will help you to hit the target if you know there positions.