That's not at all the problem here, Elite is peer-to-peer with only a matchmaking server and some services for handling the BGS, station services, etc. The second-by-second gameplay is peer-to-peer. There are others that use peer-to-peer successfully, huge games like CoD and Destiny. Neither of which have anything like the problems Elite seems to (that's not to say that they aren't without their problems).
However, there are two key points that put it firmly in FDev's court:
Why does the game bomb out with a connection error? Why isn't that handled much more robustly? For example, try different peers as hosts - if it's just not working, drop to your own local instance and keep trying in the background.
It used to work! Why doesn't it work now?
Let's see if the latest patch fixes it, but if not then I really think they need to have a concerted effort with the community to try and resolve it. Even if it means creating an open debug build to collect more data and pin down the problem. I would gladly give-up my time to help with that.