The fact that you can capture a few seconds indicates that you have a connection. Loosing the capture after a few seconds indicates the PC is not keeping up with the data transfer rate.
First thing to eliminate - check that DMA is enabled for the drive you are writing to.
What is the specification of your pc? Video capture using firewire needs an absolute minimum of 700MHz processor.
Is the disc you are saving video on the same drive that has your operating system?