Last week, my wife told me she couldn't access Prime. I checked and every other site worked fine, but Prime tried to come up, but after a few second, came up with the message stating no connection, check my router, wires, etc. I did so (this occurred on a Roku Express, but an Ultra gave the same message, both on the same wireless networks).
To make a long story short, I use DNS servers different from my ISP. When I let my router pick up my ISP DNS servers, or even setting them to Googles DNS servers (126.96.36.199,188.8.131.52), Prime worked fine. Guess my "smart" DNS isn't so smart after all. Strange thing here too, I have a VPN off of which Prime worked just fine.
'Just wanted to pass this along, possibly long known to you veteran Roku users here, but Prime has never done that before last week.