I picked up this device a couple of months ago. It is a 3810X running Software 9,2,0 build 4806-50. It gets power from a second USB connection on the TV.
Initially, it worked well with no issues. About a month ago after turning on the TV which turns on the Roku it would not respond to the Roku remote without pressing the buttons 20 or 30 times. Once it responds it responds from then on without issue until it's turned off and you start the process again. I do wait to try and get it to respond until it establishes a connection with the network although I would think that wouldn't be necessary.
I turn the TV on with the Roku remote and control volume and those controls work initially without delay. I haven't replaced the batteries because the battery strength indicator shows 3/4 full, also because power off/on and volume work and because after that initial delay it works without a problem for as long as it's on.
What I've learned since posting the original issue is that for me it is a battery issue. This means the battery strength indicator is useless as I've never seen it display lower than 3/4 full when the problem starts. Putting in new batteries fixes the problem.