Aside from the obvious network connection checks, a quick thing to check would be to take a look at the computers power settings to make sure that nothing is going to sleep after a set time (Power Options from pc control panel) I would recomend changing the settings to "Maximum Performance" and then going into advanced power settings and setting to 'Never' aany power options that send certain items to sleep.
It could be a bad network card or cable or port on the hub/swtich that this user is plugged into.
It would be useful to look at the server logs for what the server thinks is happening to that client computer when it disconnects. This can be helpful in determining the circumstances of how the client is lost to the server, and will give you a valuable data point as you track down this problem.
To follow up, please read Steven Blackwell’s description of the possible errors you might encounter:
In my experience these errors can point to a network/network card/network jack problem.
Beatrice Beaubien, PhD
FileMaker Business Alliance
FileMaker 15 Certified Developer
Knowledge Translation Certified Professional
Connection by LAN or WAN? VPN?
Could be a dynamic IP change for the client. This will cause a disconnect. The other ideas about hardware are also valid points to check.
I would definitely update FileMaker to v12.0.4. v12.0.1 was the first release in the new file format so had a lot of issues.