No, I don't get the error that frequently, although I worry if my visitors see it frequently. I have a lot of trouble repeating it. It seems to happen pretty randomly. Sometimes I don't see it for weeks.
Today however, I kept getting the 'connection dropped' message from my browser continuously. I was uploading a large file to amazon s3 on my machine at the same time, so my connection was quite saturated. (Our lsws server is not on the same network as my machine)
I'm convinced this had something to do with the error since once the file finished uploading, I could connect to our server just fine with no 'drop' errors. FYI, although slow, I could connect to other sites/servers including the lsws admin page of the server just fine while I was uploading this file, so I think something isn't right. In the past though, I haven't been uploading anything when I've received this 'drop' message in my browser, so I'm not sure if it's related to a slow connection, or I'm just seeing two different issues.
I'll try your update and see if I can repeat the issue.