@Desp suggested I switch from port 5555 to 7777 and that seems to have greatly reduced the disconnects - so far only 1 in 2 hours, where before I was getting disconnected every 10-30 minutes. I'm still seeing about 2.5% rejected shares, though, but this is likely due to my distance from the server.
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I resumed mining XUN about 26 hours ago and I am getting lots of disconnects and rejected shares on port 7777; a disconnect every 5-15 minutes, it looks like, so even worse than it was before. I am also seeing significantly lower than expected earnings for the previous 24 hours: 548 vs. a minimum of 650, and more like 750 based on average difficulty and my hashrate of 1900 H/s.
I suspect these issues are related, but a contributing factor I've identified on other pools that had poor earnings are stingy PPLNS/PPLNT settings. I don't know if that applies here, however.