HDMI cables do not do well over long distances, this is a well known limitation and is not specific to the converter. While you may find some HDMI devices a bit more tolerant of longer cables than others, all HDMI devices will eventually run into problems as cable length increases (this is especially true when using cable extenders).
Since the Mini Converter UpDownCross HD has SDI outputs, you could use a short HDMI cable from the camera into the converter and then use SDI for the long cable run (SDI does much better over longer distances as Eric-Jan suggests).
If you want to go the entire distance with a single cable, your best bet is probably to use an HDMI fiber optic cable. Since these cables convert from electrical to fiber optic signals internally they can go much longer distances with less signal attenuation. Most HDMI fiber cables are made with full size HDMI connectors at either end, so you would likely need a micro HDMI to full size HDMI adapter to connect such a cable to the GoPro.
See this thread for more discussion of different types of HDMI cables:
viewtopic.php?f=4&t=150527