Thanks for the responses. I think I’ve got it now. I feel bad for wasting your time and Tablo support’s in blaming their software. I think my router had uPnP enabled by default, and I never disabled it.
Long ago I created static port forwarding rules which I thought were what was being used, but it must have been using uPnP for years without my realizing when it finally stopped working. I have Verizon FiOS, and I know that they do push out updates to their routers. But, I thought that any update that they would have pushed couldn’t have broken a static port forwarding rule. Perhaps it broke uPnP though, and that’s what triggered it.
The GUI on the FiOS router is needlessly unintuitive and convoluted, but I found this guide by Radojevic and kennethervinyoung super helpful as I was unable to get port forwarding working without uPnP.