Just putting this out there in case it helps someone else.
My Moto X (1st gen) was dropping Wifi internet access at home. Was it the phone getting old? Was it Republic Wireless software app? Was it my Internet Service Provider (ISP) Centurylink DSL? Was it my modem/router from Centurylink (1.5 years old)? It is often hard to narrow it down but I replaced my router and that fixed my problem. I turned off the router portion of the Centurylink modem/router.
I purchased a new wireless router from Amazon. The one I chose was:
ASUS RT-ACRH13 Dual-Band 2x2 AC1300 Wifi 4-port Gigabit Router with USB 3.0
but probably any of the AC routers (the latest kind) would improve things if you have an old router. This one is a AC1300.
A new router sends out a stronger network so less dropped network connections and faster speeds. If this indeed does fix the problem, it is probably because we (and probably our neighbors as well) have been accumulating so many wireless devices (11) and Bluetooth devices (3) that there is interference at the 2.4 GHz network. This new “AC” router puts out a 5GHz network which six of our devices including my Moto X can access, and a 2.4 GHz network that the other five devices can use. It seems to be improving the performance for all the devices.