Several Kodaks have problems with the cable release which seems to "slip" over some lever when it's being pushed down. This is due to a small lever behind the cable release thread which is off-center.
There are two possibilities to fix it. One is the "traditional solution" which I usually prefer: you have to dismantle the camera and bend a lever inside the shutter mechanism (just a very slight adjustment will do since the "pin" of the cable release itself is only slightly thicker than 1 millimeter).
Unless you feel comfortable taking apart things like cameras or watches, I'd rather recommend that you keep your fingers off the shutter mechanism. If I had to repair it, it would take me about 1 to 1.5 hours - including cleaning of the lenses and re-focusing.
However, you MIGHT try the "quick solution" which usually works quite well.
Take the camera and a bright light (flashlight or even better a halogen lamp, the sun will do as well). Peek inside the tiny hole that's used to screw in the cable release (let the light shine in as well). You should notice a small lever some where on the back of the hole. In your case, the lever might very well be off-center (where it is supposed to be). If it's too far off-center, you might not even see it at this time. In the latter case, set the shutter speed to B and cock the shutter. Then press the shutter release button and keep pressed. NOW you should see the lever.
All you need is a tiny little screwdriver to put through the hole and to bend the lever until it's in the center.