I've had similar issues with my Sony DCR-HC28), as have many others with many kinds of camcorders (see
http://forums.macrumors.com/showthread.php?t=188067).
One day it was working fine without any problems. The next day imovie didn't recognize it. I tried various recommendations: turn camcorder on before starting imovie, turn it on after starting imovie, make sure it's plugged in, run software update, repair permissions. No luck.
Then I found some ideas from Apple:
iMovie '08: Cannot see or control camera
http://support.apple.com/kb/TS1059
What to do if your computer won't recognize a FireWire or USB device
http://docs.info.apple.com/article.html?artnum=88338
I opened System Profiler, clicked on Firewire (w/ the device plugged in and on) and it didn't recognize it. Then I followed some of apple's instructions. Turned off computer, unplugged it from wall for five minutes, disconnected all usb/firewire things (printer, etc) except for the keyboard. Then rebooted. Plugged in camcorder to firewire. Turned on camcorder. Opened System Profiler, clicked on firewire and sure enough, it recognized the camera. Opened imovie and I was back in business.
It's been working fine since then. Hope this helps you.