It is possible that over time your SDHC card has become fragmented. You can fix this by using the menu of the Panasonic to initialize the card. It would be best to try this with an empty card, because if you initialize the current card, you will lose anything that is on it.
If you need to get clips off the current card, and iMovie is not seeing them, I would suggest that you close iMovie and open Disk Utility. Select your card in Disk Utility and create a disk image of the card. Now, mount the disk image and see if iMovie can see the disk image. This may not work, but it is your best shot.
You also might try trashing your preference files (although I think this is less likely to help, it is easy and can't hurt.) See here for how.