I will check the other steps as you suggest.
As for Dropbox being available offline, please note my point that the behavior is sporadic. It wasn’t finding the files, and then it was, then it wasn't. (N.B. Now, the next morning, all Dropbox-located folders are appearing again.) At no time in that sequence did the online/offline status of a single Dropbox file or folder change. Also note that Spotlight is finding everything consistently. HoudahSpot was, then it wasn't, then it was. It ain't Dropbox.
The loss of the Contacts cards from search corroborates this. Contacts are on the root drive, not Dropbox. If it were a Dropbox online/offline issue, the Contacts cards would not have disappeared from search results.
I don't believe it's even related [much] to Alfred. It seems to be a Spotlight indexing issue.