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I'm on 17.1 beta 2 and the issue still persists for me in that my messages are not downloading anything past 9/28/2023. I've done this:
Settings app, tap on Messages, tap on Siri & Search, turn off all of the settings shown, restart the iPhone, and re-enable those settings in order for the issue to be fixed.
I can confirm that it made no difference at all. I'm hoping it just takes time but it's been 30mins so far with no downloading of messages. I know they are all there because I can see them on my MacBook Pro.