Well, it should really only happen when we restart our servers, which isn't often at all. So, there's something else cutting the connection for you. In some cases there are home routers that cut connections, in other cases many countries/jurisdictions don't like neither SSL traffic nor mining traffic. May I ask where you're located? You can PM me if you want to. Also, I'd love to know what version of TRM you're running? We have noticed a higher degree of short-lived inbound connections lately, but can't explain why.
people start autotune, notice they didn't set their own wallet and stop the miner? Just a thought.
There's an easy way to test if this is the case. set a minername in the batchfiles that come with the miner.
If they forgot to change the wallet, likely they didn't change the miner id either.