During game play the computer reboots. It always happens with this game and we have no problems with other games.

Hmm, just that game huh?
Then it has to be either badly scratched up or in need of a good cleaning.
Gamecube discs are rather compact so the data can be damaged and odd errors and even graphical artifacts are very common with Gamecube games.
It's best to take the utmost care with these small discs.

Distilled water and a soft computer screen cloth can be used for a quick wipe down to remove any smudges or bits of dirt clung to it. Not a whole lot of water, just enough to make the cloth damp or a little wet.

As for scratchs I'd suggest using one of many scratch cleaner tool methods or as a last resort find a gameshop that does disc rebuffering.
With a small disc like that it can be a little hard to buffer scratchs out yourself.
Most gameshops charge a moderate fee for rebuffering and resurfacing discs and usually do the smaller sizes aswell.

I'd also suggest cleaning the disc drive laser less very very gently with a q-tip but from what I can gather from your problem, that shouldn't be nessecary.

Hope that helps.
Good luck and have fun with the game once you fix it up. (One of my favorites really.)