Duct tape to the rescue!
Joke aside, a piece of black duct tape length-wise over the remote back will hold great the cover to the remote because of the cover's particular design. I just looked at three Roku remotes i have and while cover design had changed, they have this in common - there are tabs sticking at front that are prone to breakage - but there are also other tabs at the back that will hold the lower end in place - so all that needs fixing is the mid-section with some tape.
PS. oops, my bad! i was answering about the current RokuCo. product - the Roku video streaming players - and now i see yours is in "SoundBridge" which is an old/legacy one - i have no clue about its remote