First, have you made sure in your Admin console you don't have the Server disconnecting inactive users after an amount of time that is too short for your needs. Second, FileMaker is a continuous connection unlike http web connections. So any break in the connection disconnects everything and you have to log back in. This means your network needs to be stable and FileMaker would be sensitive to bad switches, routers or ethernet wiring, etc. Do you know about the health of your network? You said all of the ones loosing connection are going through ethernet lines to a server. Obviously they can't do that directly and so they are going through a switch. I would swap out that switch with another one for a day and see if it makes a difference. Dumb switches are pretty cheap anyway. But give that a try.