Cannot discover Sonos Move on new Wi-Fi network.

This is a common situation and there is no “one size fits all” quickie suggestion. We need a bit of info. Do you tend to spend time at one or the other home, or are portions of your family simultaneously living in both houses and using the SONOS components?

Each SONOS system is known as a “Household” and a given unit can only be a member of a single Household. It is possible to have a Household split between multiple physical locations. A split Household is less hassle when shuttling units between homes, however, some music services will not allow simultaneous use at both homes. If you primarily use MOVE and ROAM as Bluetooth speakers at one or both of your homes, Household does not matter after initial setup because music is played directly over the Bluetooth link. Do you use the same WiFi credentials at both homes?

Don’t Factory Reset anything without further consult.

Just to also add the mobile hotspot mentioned in my post above cannot be running on the same mobile device as the S2 Sonos App - use an entirely separate mobile device for the WiFi hotspot.

Easiest method however, is to simply setup each router with the same WiFi SSID and password credentials. 

…or it might be asleep, or even an SSDP discovery issue, if multicast packets are not getting through from your mobile controller device to the network segment that your ‘Move’ is using.

I would first see if you can ‘ping’ the device across the LAN, or see if it’s connected to the local WiFi when it has disappeared from your Sonos App. If it’s not connected, then check if it’s asleep, or powered off. If it IS present on the LAN, then see if it can be seen by another controller device (if you have one available) linked to the same WiFi network, or just see what happens when you toggle off/on your existing mobile network connection to the LAN or switch between its WiFi bands.

Note, sometimes having multiple WiFi access points, extenders, power-line adapters etc. as part of the wired/wireless network setup, can also sometimes cause issues with multicast packets for device discovery. Some network switches may also cause problems too and to complicate things further, so can security software on mobile devices, such as VPN clients, Firewalls, MAC Spoofing, WiFi Calling etc; so you may need to explore quite a few things to get to the root-cause of your issue.

I don’t think this will prove to be an issue with your Sonos Move and I certainly would not jump to that conclusion until you have perhaps explored the other things briefly mentioned here.