When the server goes down, the entire match will disappear, because there’s no server for it to exist on at that moment. The message will usually say “unexpected server error.”
When you’re disconnecting, is there an option to rejoin? If so, then it’s a local connection issue (in your home or on the route to the server). This message usually reads, “client requested disconnect.”
Edit: I’ve only seen a handful of the same people reporting connection problems, but I rarely see anyone drop from my games across Quick Play and Competitive modes. It doesn’t seem like disconnections are common for players in North/South America. As for players in other regions, I’m not sure about their experience since they have separate forums.