HDMI Splitter: outputs affect one another?

Hi folks,

I'm confused at how my HDMI splitter outputs appear to be affected by one another.

the setup:
A single video source connects to a monoprice splitter, which outputs to (1) a projector and (2) a TV.

Strange behavior:
If both the projector and the TV have the correct input selected, things are great. If, however, the TV selects a different input, the projector immediately loses sync. The projector does not lose sync if the TV is turned off.

details:
the source is a ps3, the projector is a panasonic ax-200u, and the TV is the LG 42LH30. Both projector and TV can accept 1080p, and the problem is asymmetrical (that is, the TV is not sensitive to the projector's state).

Any idea what could be causing this? I'd be very grateful for any insight!
Thanks,
-Vin

That makes sense, as does your suggestion to use a switch instead.

I should probably have mentioned that the source-to-splitter cable is currently 28AWG. I'll probably try using 24awg cabling, and if that doesn't fix the issue I'll just replace the splitter with a switch.

Thanks a ton for your help. This forum is awesome!