To illustrate what I am seeing I just ran a single gekko stick at kano and bitminter for the same amount of time (couple minutes), look at the hash rate difference (stick should and has average 12-14GH/s) and also the work restarts when pointed to bitminter.  Note this is not the miner receiving new work, this is something different that I have only experience since pointing the sticks here:
 

I will try the other servers and see if that changes the connection drops, but I've never had that happen at other pools.  I made no changes to my gear or setup (that have been running for months) other than to point them at bitminter.

Hash rate shown in the shift page appears to be more accurate as you stated.  For the first 2 full shifts my total hash was about expected, just a little lower than it has been historically, but the next two look at the loss of hash, this is what I'm trying to figure out.