For the last few days, at least once a day, My internet has gone out while playing an aram match and instead of the game reconnecting after the internet comes back online, I have the reboot the entire game to connect back into the match.
This issue has existed pretty much since HotS has. The game and servers do not like it when your global IP address changes while connected, which usually happens when consumer internet connections are reset. Restarting the client reconnects to the server from the ground up with the new IP address, allowing the match/play to be resumed.
Fixing this is likely non-trivial as at the very least HotS would need to coordinate with the BattleNet application to retrieve a new login token for security purposes. This currently implicitly happens when you restart HotS.