KSP is a quite difficult game. It would be impossible if the target was actively trying to avoid you.
As I said, just don't program the AI to do that. Problem solved for single player. Any player doing that would work themselves in a stalemate, not the most fun of situations, I couln't really imagine a player doing that unless they were trying to troll, or something. The solutions to the problem below would also help with this problem.
Also, not that I think about it, this same problem applies to regular atmospheric flying games. If you both fly the same plane in the same enviroment, you should have the same acceleration and top speed, making an unreachable target entirely possible there as well.
The problem with games is rarely that too much is happening; it is usually that not enough is happening. In frictionless space, it is far too easy to over-accelerate and miss all of the action. There needs to be some mechanism to keep people where the fun is.
I agree, but there are a number of solutions I can think of. e.g. The game is actually a futuristic sport, with a big shield dome limiting the arena size. If you go too fast, you just crash. Don't go so fast next time (this is where the player starts learning to play the game). Or your trying to take a moon-base (and as such would encourage the player to actively avoid accelerating past the target). If you shoot past your target, just slow down relative to the target. It should take about the same distance to slow down as it did to accelerate, so you would have had to have been an extreme distance away from the target in the first place.
If you do somehow get unreasonably far away, just kill the player ("You were lost in the depths of space", or something). You would learn how to avoid situations like that, just like you learn how to avoid slamming into the ground in any aeroplane game.
Additionally, extremely high speeds could put serious strain on the engine, depending on the amount of stuff in space. I don't really mind the constraint, although it does seem a bit arbitrary when you suddenly hit 103.5m/s, it's easy for my WSOD to dismiss it.
The above solutions also largely solve this problem. Using an arena dome limits your top speed. If you are travelling at high-speeds past the moon base, there is nothing out there (because space is quite vast and empty, there really isn't a whole lot out there) and there shouldn't be any physics issues because of that.
Regardless, the physics don't have to be realistic at high speeds. At those speeds, its reasonable to assume that any collision will result in your explosion, and as such it doesn't have to compute a physically accurate response.