That's a Streambar, right? I have one of those, and don't have any issues with the remote. There are no headphones involved, so it can't be that causing the problem.
Shooting in the dark here, but how strong is the wireless/WiFi signal in that room. The remote is Wifi Direct, and will communicate with the Streambar on the same channel as the Streambar is connecting to WiFi. If the signal is weak, or has a lot of interference (from other networks on the same channel, for instance) it could make it work harder, draining batteries, but I've not seen Roku acknowledge that.
Perhaps others that have had the issue that was resolved may offer additional insight.
DBDukes http://www.dbdukes.com/Roku Ultra (4660) Roku Streambar (9102) Roku Streaming Stick+ (3810)