I went thru a stretch like this with my own network, with a wired connection to my own router. I found re-booting the router fixed it most of the time. It might also have been a problem at the game server's end. Certainly you're not the only person complaining about disconnection problems the last few months. Maybe log into the DBG forums and see if others have similar problems and found fixes. It may be harder to reboot your neighbor's router whenever you need to but I'd suggest at least starting with that.
How's your wireless signal? If it's weak (since you're "borrowing" from a neighbor, it could certainly be) that could contribute to latency problems. Latency affects quality of game play and can cause weird problems like inordinately fast movement, delays in fighting, etc, which can affect other players' experiences so surely DBG will kick you if your latency gets too bad.
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