I should have said I have the same (or close) symptoms. Let me clarify. Plex workarounds aside, I can use Plex on the house LAN and even on the WAN (Plex app on the phone). What I can no longer do is use it with Alexa because I go into a “Sign in” infinite loop when I try to link the account. A number of days ago I could no longer play music via Alexa (effectively “Ask Plex…” resulted in “Uh oh, something went wrong…”). As a last resort, I disabled the skill on the phone and then ran into the (new) “Sign in” infinite loop.
I read somewhere that I could link the account using a computer, but I could not figure out a way to do that. Next time if/when I talk to AMAZON I will ask if there is a way to do that. At least then I will get a better look at what’s failing. Once (if ever) I am able to link the account, I may still have the original “Uh oh” problem. I did nothing that I know of to cause any of this. Plex under Alexa just abruptly stopped working.
I manually disabled the skill – it did not time out. And it’s never timed out before. My experience with Plex and Alexa together “over the years” is: in the beginning, it did not work well at all. Then it started working. Then stopped. Then started. Etc. For a good number of months now it has been working, and then, all of a sudden, it stopped in the last week. AMAZON basically disowns the problem, but the last I heard they will look closer at the Plex-Alexa protocol to see why it may be failing now. It appears AMAZON is not being flooded with complaints about the problem. And there may be two problems – the new “Sign in” infinite loop and perhaps something in Plex with the Plex-Alexa protocol. I don’t know. No one says what’s really going on under the hood, so I can’t figure a workaround if one even exists.
I resist reporting “bugs” in, or in general even using, this forum. I only checked it to see if anyone else experienced the problem. I don’t see a lot of chatter here or from AMAZON on this issue. And, again, I did not do anything I can recall to bring this all on. I do know I can no longer use Plex with Alexa, and see no fix(es) in sight.
P.S. I am using an OLD Plex server (on Windows 7) and an OLD Plex client (SHIELD). I “froze” these versions when I got both to work together relatively well on the LAN. Since then, Plex no longer even supports updates to the server on Windows 7 (unless that changed). Up until just recently, this setup has worked on the LAN and on the WAN (Plex app). (Actually, curiously, I have two phone lines and two Google Pixel phones. On one phone movie subtitles do not work right, even though I’m using the same current version of the app on both phones. And music does not work on either phone. I never complained in this forum about this app music problem. I’m just mentioning it in passing now. With Plex-Alexa on the LAN, I play only music, and it worked until sometime in the last week.) I have always (with workarounds) got Plex to work on the LAN. On the WAN (phone ISP), movies, but not music, basically work.