Nikon d40 works intermittently?

I have a nikon D40 which recently started to work only on an intermittent basis. When I depress the shutter button it simply does not shoot. Then it works for few, then it doesn't. Any suggestions?

Where are you attempting to shoot - in the dark? The camera can't focus in the dark and won't fire.
Barring that there could be a mechanical / electronic problem. If that's the case call Nikon for advice.

A common problem with the D40 and kit lenses are the electrical contacts for the lens. Dirty/oxidized contacts will prevent the camera from autofocusing which prevents the camera from taking a shot (the camera must be in focus before it will take a shot).By rotating the lens base back and forth a few times (just until it hits the stops, do not use undue force), this will clean the contacts. See if this helps.

Also, be sure your not trying to focus on a featureless object like a plain wall or a cloudless sky. The focusing detector requires contrasting edges to autofocus.

That's usually caused by focusing too near from the subject (closer than the minimum focusing distance of the lens) or when you are trying to shoot in low light (where the camera can't see a thing already).To test the camera still works perfectly, set it to Auto mode, Auto ISO, AF on, EV 0, and White Balance Auto. Go out an find a brightly colored parked car under the sun. Stay a good 10 feet away from it and take a shot. If the shot is good, take from another angle, and yet another angle. If the camera works perfectly each time producing decent to fabulous results then you have found the problem. It's you.

If the camera fails, bring it in for servicing to the nearest authorized Nikon service center in your area.