can i hook up a 4 to 1 component switch to my projector?

i have an infocus sp4800 projector with only one component in and i want to hook up my hd cable box and my progressive scan dvd player to it. both work fine by themselves hooked straight to the projector but when i hook up a component switch to the projector it has a perfect image at first but after a few minutes the screen goes blue and it sets up the image again. it sets up the image and the picture is fine for a few minutes and then the whole thing starts over again. i've tried 2 different component switches and both had the same effect. i would appreciate any input. thanks