MMS images were offloaded; cannot download again

I received some MMS images a few days ago. They displayed fine at the time I first received them. When I went to review them a couple days later, I saw they had been offloaded from my device. Tapping on the images to re-download them fails—it just sits stuck on this “loading” status forever. Force-quitting all apps (including Messages) and rebooting the phone does not resolve the issue.

My on-board storage has been somewhat full recently so I think my phone is being aggressive about offloading images from the Photos and Messages apps (which are synced/backed up to iCloud), although it’s a bit surprising to discover that tiny little MMS messages would suffer this fate nor be so difficult to restore.

These are important images (I need them for a claim) but it seems I may be stuck unable to ever recover them. What gives and how can this be resolved?

I’m running iOS 14.3.