It sounds like whenever TimeCapsule runs it is taking over the connection so nothing else gets through until it completes. Client connections to FMServer trying to read or write may be unable to get to their connection in the meantime, and FileMaker on the client machine is "timing out" before the bandwidth is freed up.
Is it possible to connect the TimeCapsule disk directly to the computer being backed up via FireWire or USB, if, for instance, the disk being backed up is on another file server? That should remove the TimeCapsule transfer from the LAN traffic.
it is not possible to connect with with the time capsule other than lan because the filemaker server machine is in a different room.
Could it be possible to limit the bandwidth time machine asks?