There's not enough light for your camcorder to record. What's happening is the same thing that happens with a camera. When the light dims the camcorder can either open up the aperture, gain up the sensor (i.e. increase the ISO), or use a slower shutter speed. In these situations that you're describing the camcorder has already opened the aperture to the max (larger opening to let in more light), and set the gain to it's highest level (so that it's more sensitive to light). All that's left is using a longer shutter speed. If that speed falls below 1/30 of a second then moving subjects will be blurry.
Unfortunately, all video equipment has the same issue. If you spend more money you can get a camera with a better lens (and a larger max aperture) and a sensor that can gain up higher. But no matter how much you spend you have to realize that when it gets dark you're going to have trouble.
The only realistic solution is to add more light. You can use the built-in light on your camcorder (if it has one) or you can buy an external light.
Some camcorders have an infrared option where it shines an IR light into the scene to supplement the available light. Generally these videos look green but some are black and white. This is really nice if you don't want to disturb other people with your light (like on a ride). You can also buy more powerful external IR lights to extend the range of your camcorder. I have a Sony that uses this technique and I use this mode a lot at the parks.