Apparently, Dropbox has dropped support for public image hosting. This sucks, but at least they're allowing me to keep all my old image shares active, so my older Moho forums posts should still display my Dropbox images.
To fix the image above, I went back to using Imgur. The last time I used Imgur was over nine years ago, so I had to reactivate my account, re-verify my email, and change my password. Once I did that, I was surprised to see many images from nine years ago and older still being hosted there. (Lots of Scareplane behind-the-scenes screen caps, so that was definitely a long time ago.)

Anyway, Imgur is still free. To use it with the Moho forums, just drag and drop your image, click on the three dots, and choose Get Share Links. Click on BBCode (Forums) to copy the link and then paste it directly into your Moho post.
Update for Dropbox issue: I updated my shared image from last week and saw that there's a range going back farther where the images are still broken. Based on something I read elsewhere, the cutoff began with images uploaded since March. Unfortunately, I'm going to have to leave those posts alone and move on.