I'm trying to win race 3 just for the heck of it, but my turbo speed keeps cutting off seemingly at random. Is it supposed to do that? It's very annoying.

Yeah, the turbos are supposed to cut out, its the same as when your free roaming and decide to use a turbo. Just learn to time the turbos just right and to shoot 'n' slow down your opponents. :D

I suppose he didn't mean boost, but the "jet engines". They drop out on collision sometimes.