There's not a good answer for this, but there are some options.
1. Try to lower your resolution to 480i, 480p, 720p, or 1080i instead of 1080p and see if that helps.
2. Replace the cable - it is unlikely at 50' that you need a booster.
3. Try a CAT-5 solution. For whatever reason, you get better distances via CAT-5 than you do with HDMI.
4. Try using a local source directly to the projector to ensure that the source/projector works together.
5. Try connecting the source directly to the projector. If you are using a 50' HDMI cable, but it is connected to a receiver, and the HD source is connected to the receiver, then you have something between things. Try a direct connection.
What brand/products/cable are you using?