To clarify, does Echo Dot become unresponsive after an hour of inactivity?
Have you tried restarting your device to see if you continue to experience this issue?
To restart your device, just unplug the power adapter from the device or the outlet and then plug it back in.
I also recommend checking to see if your Echo Dot is up-to-date with the most recent software version available. You can say, "Check for software updates," to ask Alexa to download and install the latest software updates available.