My 3600x has recently started freezing after it has been idle for a while. When I turn off the TV for a few hours and then turn it back on and switch to the ROKU it gives me a screen stating that it needs wide bandwidth connection etc. then switches to the home screen showing "Not connected" at the upper right. It will not respond to the remote. There is a good strength WiFi signal available. The only solution to the problem is to press the reset button on the ROKU. Once reset the Roku recognizes the remote and works fine until I either turn off the TV or use another device for a while.
Roku 10.5, currently rolling out, has added a new Power item in the Settings > System menu for some recent Roku models. In my estimation it is not well thought out. If you have this Power item, under "Auto power savings" see if deactivating "After 20 minutes of no interaction" fixes the problem
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I unfortunately do not have that setting. It is acting like the system is going into a sleep mode when the TV is turned off. When the TV connection is re-established the unit does not appear to reconnect with the WiFI.
Try again verifying that you do not the Power setting mentioned by @makaiguy that may be located under Settings..System..Power..Power Savings.
Also, try using the power adapter plugged into wall if currently not using rather than TV USB port.
The "No Signal" seems to be more power related, while the "No connection" is more network related. You could have a couple things going on simulataneously.
If you are using a mesh network, it could be that the Roku and the WiFi Direct (the mini network used for your remote) are having problems maintaining connection if they are being switched between bands by the automatic router management. (just kind of lose each other).
Try connecting your 3600x to the 2.4ghz network and still if connection stabilizes. If it does, then try setting a manual wireless channel within your 5ghz settings to either 36-38 or 149-161, rather than using "Auto" channel. When left to "Auto", there is an increased chance that the router will select an incompatible wireless channel on the 5ghz band. (Roku cannot use/see DFS channels 52-140 so Roku will lose connection).
Post back with an update and include router model number and ISP (internet provider) if you need more help. Provide what seemed to help/not help, etc. in regard to the above steps. Any router settings you can ascertain would also be very helpful.
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4) Tied into a 2.4ghz network signal. Deliberately set up as a 2.4 network.
5) I am using a TP-Link 1750 tied into Wave Internet through an ARES Surfboard SB8200. I did recently move but the problem did not exist until the latest software upgrade. The wireless modem is the same one I have been using for a while with no issues. All other wireless items are having no issues.