There is a known issue where when you tap into a poll or bulletin from the Home Screen, you cannot archive it.
Here's how to get around it:
Tap on Chatter
Tap on the Team with the Poll or Bulletin
Tap on the hamburger menu to open the Poll/Bulletin viewer
Tap on the Poll or Bulletin you want to archive
Archive the Poll or Bulletin from here
This should allow you to archive properly!