UPDATE: This has now been restored at Microsoft's end, which is good because it shows they still care, despite the end of official support for Lumias. However, it's worth grabbing the patched version anyway, as a) it works just as well, and b) it'll come in handy when WDRT goes 'out' again!
Original news story follows...
Windows Device Recovery Tool has been a Microsoft staple in the Windows Phone world for a decade. Essentially it looks at what's connected (e.g. a Lumia 735 below) and then looks up the latest official firmware for it (as in retail software shipped in the phone when new just before it stopped being made) and installs it, wiping the entire phone but letting you downgrade gracefully from, in my case Windows 10 Mobile to Windows Phone 8.1. (Yes, yes, look elsewhere on this site (e.g. here) for tutorials on going the other way around!)
The first thing the tool does though, is check on Microsoft's servers for an updated version of itself - and this is currently failing. It's not clear whether this is permanent or whether Microsoft will care enough to investigate and fix it, but given that all versions of Windows Phone and Windows 10 Mobile are long out of official support, I'd bet it's not a priority in Seattle.
However, some helpful person has deconstructed WDRT, hacked out the line of code that phoned home, and then reassembled it. There are copies online in many places, but it's also up on my OneDrive here. Obviously, grab it at your own risk - I checked it for malware, but there are zero guarantees and we take no responsibility if somthing goes wrong, on your PC or on your connected phone!
So it seems that the only bit broken at the moment is the WDRT update check, but if this is indeed Microsoft's servers gradually 'forgetting' about Windows Phone then the next stage might well be that the OS images (FFUs) will disappear from Microsoft's servers too, which complicates things still further. If you're worried about this or if you're reading this significantly after Spring 2021 then it might be worth you either archiving the firmware for your specific phone from LumiaFirmware or by using WDRT and then copying the contents of the (by default hidden) relevant folders in C:\ProgramData\Microsoft\Packages...
If some of these articles are getting a little techy then sorry - but at this stage in Windows Phone 8.1's life, in particular, all that's LEFT is hackery and DIY solutions. It comes to all platforms a few years after official support ends!
Data points welcome on how you get on with this tool - the download size and installation all seem 100% legitimate to me, but - again - no guarantees!