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Actually.. losing connection depends on how long you stay in the lobby after: 1) Leaving a game
2) Entering B.net with a char
So even if you stay in a room for.. let's say 1 hour, but you leave the room, stay in the lobby for 1 second and switch chars, stay in the lobby for another 1 second and enter another game, chances are, you'll get realm down after 5-10 entering/leaving. so try to spend 5-10seconds everytime you enter the lobby.
If you are versatile enough you should try loosing some time doing other runs than meph runs, such as pit runs. If you are a cold only sorc (which you may be because you're only doing meph runs), try the ancient tunnel in the forgotten town, it's a level 85 area without any cold immune at all. otherwise do the usual runs at the same time like A5 superuniques, Andy and the other pits.