Q: Mail rules not working...

Yes,

if all of the confitions are met

Every message

Date Received is greater than 31 days old

Perform

Move Message to mailbox Archive

should do the trick, even if you've read the message on another device in the meantime.

unfortunately, doesn't work for me.  Absolutely nothing happens.  It worked once and then it stopped.

Had this same problem with OS 10.10

This worked for me, after nothing listed above did work:

1. Under the rule News From Apple I removed "Stop evaluating rules"
2. Under my rule I added "Stop evaluating rules"

Hope this helps somebody; it is infuriating when something like this happens out of the blue.

This solved the issue on my case!!

Thanks so much!!

Message rules Mail 9.3 not working, this is an on going problem I expect to see a resolution..!

How do you know?

Still seeing this in Mail 9.3 (El Capitan). No resolution yet.

Neither the mark as read, nor the move to mailbox are working.

You might want to consider starting a new discussion. Since this one is a couple of years old, less people are likely to look at it. A new post would be much more visible. You can link to this one. Post in the El Capitan community.