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I posted a second reply but it hasn’t gotten up yet because I am still a new member. In short:

It was the 10.4.9 upgrade for OS X (from 10.4.8) that caused the problem and this is documented by many other people who are using FCP 4.5 or earlier and OS X.

I did a reinstall of OS X 4 and did not upgrade to 10.4.9 and it is running perfectly. I just digitized over an hour of continuous footage with no problems.

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First off, if you think it is the RAM, have you tried using the apple utilities on the OS X install disk? If you reboot with the DVD in the drive and hold down “option” it will boot to the tools that you can use to check if your ram is damaged.

I am having the same problem but with different hardware. Here are my specs:
FCP 4.5 (HD)
Quicktime 7.1.5
PowerMac G5
Dual 2Ghz
2GB RAM
OS X 10.4.9
Two internal SATA 250GB Maxtor Hard Drives
Sony AG-DV2500 DV Deck

This is the first time I have ever had this issue. I have:
Reinstalled Final Cut
Cleared the disks and now have 150GB free on each
Tried capturing to each drive
Tried several different tapes
Swapped out the firewire cable
Run the utilities on the OS X install DVD to check the RAM and Hard Drives
Disabled the warning about dropped frames (it then captures the video and audio out of sync)

It drops frames after only capturing 10 or 15 seconds of footage. I have used this system for almost three years now with never running into this problem before.

Looking at the software update log (Apple/system preferences/software update/installed updates) the only thing that has been installed since the last time I captured without any problems was quicktime update to 7.1.5 and Mac OS X updated (Power PC) to 10.4.9

My guess is that it is one of those updates that is causing this problem. Have you installed these updates yet?