I wanted to post this for anyone struggling with screen mirroring issues ranging from failure to connect / random disconnecting / and severe screen lag. I have experienced all of these issues with both my 3600RW and 3810X screen mirroring my Windows 10 laptop PC.
For me the issue was that the PC and the Roku were using different Wifi bands - 2.4 Ghz and 5 Ghz. I solved the issue by configuring my router to split my Wifi networks into separate 2.4 Ghz and 5 Ghz networks. Then I ensured that both the PC and Roku stick were connected to the 5 Ghz network and voila - the connection now works on the first try, stays connected, and has virtually no lag (as good as Roku mirroring can really get considering its limitations).
Might not be a panacea for all circumstances but worth trying since I tried literally everything else to resolve this before this worked.