If one is splitting the HDMI, then only ONE output will have all audio data pass, while the other will be limited to stereo at best. This is intentional and part of the HDMI spec. However, this imposed limitation when splitting HDMI can also result in all manner of annoying problems with audio such as you are experiencing.
FWIW, I have my AVR now outputting from BOTH of its HDMI outputs: on to the big HDTV, and the other to the 23" HDTV for when I listen to music but need a TV to control the interface while audio streaming listening to SACD with Blu-ray player. Now, when I am watching TV, the little TV is off and the big TV is on. If I change an input of the AVR in this mode, then the big TV will NOT display a stable picture but blinks instead--UNITL I turn on the small TV and then both TV's display stable pictures. I can then turn-off the little TV and watch big TV again with stable picture.
HDMI spec is about protecting content FIRST, and everything else second and subsequent. I supoose if HDMI were a person it would say,
"We are HDMI; HDMI is designed to make such set-ups painful, and in the case of audio, to degrade one of the split outputs. This is HDMI; we make simple HONEST set-ups difficult by design. What? you want to SPLIT the HDMI out. What are you a pirate or crook? Who would have a possible need to mess with the copyright content we are designed to protect in such a way? Are you up to no good? Well, you can go back to analog for such shenanigans. What? Analog connections hard to find these days and offer inferior quality. Well, yeah! That's how we've planned and enforced it. You mad at me? Well, soon, you won't have me, HDMI, to kick around anymore as everything will be available ONLY on the cloud with all sorts of tech to make recording impossible. So, bet you want me to stay, after all, huh. We are HDMI!"
Although it provides the efficiency and cleanliness of a single cable connection for video and audio and bandwidth for sound with no loss when mixed at the studio, HDMI can also be a pig PAIN ITA. Your problem is exactly as HDMI wants it.