The game does not run via the server, but via a peer-to-peer connection between the two players, whose clients simply send each other their inputs. If it works like IV, then replays are only sent to the server afterwards, which explains why a disconnect results in no replay. This has the advantage of giving you a faster connection, since you are connected directly to your opponent, but comes at the expense of one player's poor connection affecting both players, and is probably subject to more issues since firewalls / routers / etc. are more likely to interfere.
However, since in V you are connected to a server all the time anyway, it should certainly be possible to detect the case where one person is disconnected from both the match and the server, for example because they closed down the game.
SFIV handled this properly, despite not having the same persistent connection, so it is probably mainly a problem of Capcom shipping the game before it was ready for prime-time.