Picture Resolutions and TV dropping out

Hello, I just bought a new Sony 4K TV for one of the rooms in my house.  There was a problem with the picture dropping out.  This was connected to a Genie mini from a HDMI splitter with my home theater which has a Sharp 1080p projector.  The projector was also dropping out.  My A/V team felt it that the main Genie should be on the new TV and now using the Genie mini on the theater and the living room TV (Pioneer Plasma 4K). Now the exercise room is working just fine, but the living room TV is dropping out.  This plasma is 1080P.  The installer said to leave both on 480P and 720P only and leave 1080i and 1080p unchecked.  He was thinking my TVs are not capable of 1080p, so I checked the manuals and they are.  When I went back to check 1080p, it says that my tv does not support this resolution.  Whether checked or not, the signal seems to keep dropping out periodically with the screen going black.  When this happens, it doesn't come back. The only way to watch the TV is to turn off the whole system and turn it back on.  I've tried rebooting both the Genie and Genie mini but this has not resolved the problem.  Is the issue really the signal splitter and must I order another Genie mini for the third room?