Can you access it via the WeatherLink (e.g. 6.0.5) PC software? Under the Setup menu you should be able to view the IP address. (under the Communications Port option)
Can you access that IP address with a browser (e.g. Edge, Chrome)?
If you can run something like Angry IP scanner, can it find the WLIP? Enable the "MAC Vendor" under the "Fetchers" in order to see Davis Instruments under the listing.
If you can find the IP address, does it show up in your Router? Is it using DHCP or fixed IP address?
The router could be dropping it when the lease expires. A reset would force a new IP address to be picked up.
Just some ideas to start. Others might chime in with more ideas.
Greg H.