I'm having the exact same problem, using the desktop app on a Windows machine. This behavior only started manifesting a couple days ago, and I'm having to relog into the app every single day after it fails to open correctly. When launching the app, I see nothing but the blue screen with the Pandora logo where it simply hangs - no error message whatsoever, and then if I close and reopen the app it will prompt me to immediately log in and then work fine. Nothing whatsoever has changed on my side, this is clearly a problem on the Pandora side.
Previous behavior was that it would resume playing on whatever song I left off and then continue. It seems very likely the servers are rejecting or invalidating whatever cookies or data you are using to retain this information, causing the player to hang, and then forcing a complete relog in. Of course, Pandora has had problem with broken or terminated server connections for years, so that is no real surprise. They never forced a relog in though until now.
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