Based on what you have told us I would make a very simple suggestion and that is to try a different cable. We say this because your computer probably has Firewire 800 ports and it may simply be a matter of an inferior cable and you'd want to try a higher end one. Specifically, you should look into the Belkin brand of Firewire cable for this connection as we have seen good luck with those on the older DV cams.
This should help to resolve the issue. If this is an urgent technical support matter, please feel free to contact us at your earliest convenience through our Support and Service web site.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM