Doesn't make sense that a limit is causing the problem. It did at first, but now that you gave more data, I doubt it. First, it would give that specific error, and second, it would only disconnect ONE device, not both. Do you have any other apps you use often on the Roku? ESPN? Netflix? If so, can you activate all 3 of those at once?
Also, does the Roku keep logs of any kind? Is there anywhere we can look to see why the Roku thinks it's disconnecting? I found this, but it seems very technical.
Last, have you tried checking your router logs? If you don't know how, reply with what model router/gateway you have and I can see if I can find the specific instructions.