I'd highly recommend that you take your file offline and remove the need for the 3G connection at all. It sounds like you're never going to get reliable connections, and you're opening up yourself to all sorts of other issues (data loss from non-committed data, record corruption, etc..) as your connection drops out, on top of your user frustrations.
There are numerous sync solutions that are designed to sync between a FileMaker server and FileMaker Go device. This would allow you to reliably have your users enter data in the field offline, then sync the data back to your server later when they have a more reliable network connection. This would also immediately solve your dropped connection and re-login issues.