I decided to bypass the hub and plugged the digicam directly into one of my computer's USB ports. Since doing this, I've had no further problems. I can now download JPG images and AVIs smoothly without worrying about whether ImageCapture is going to quit all the time.
[Editor's note: This is generally good troubleshooting advice as well. When you're having a problem with something, try to make sure it's as directly connected to your system as possible to eliminate intermediate causes. I had a similar issue with a USB switchbox that went flakey a couple years ago...]

