Still not sure why (as the WiFi here didn’t change) but I had the LED of my ScanSnap ix500 scan button light up orange instead of blue.
Via How to Connect More than One Mobile Device to Your ScanSnap iX500 [WayBack], I found out it means this:
If the light is orange, go to the ScanSnap Wireless Setup Tool and check the mobile connection.
So I hooked it up over USB and re-registered it to the WiFi connection. You can do this from both a Windows PC and Mac:
If I ever want to use it on Linux: it is possible to get it to work, see 12.10 – Does the ScanSnap IX500 work with Ubuntu? – Ask Ubuntu