There are a handful of Android phones which use the same chip for WiFi and BLE. As a result, you will frequently lose connectivity to WiFi and have to rely on the internet connection you get through your carrier.
We have been working on compiling a list of phones which we know have this issue and which we know do not.
The following phones are known to be problematic: Nexus 4, Nexus 7 2013 Edition, Moto X, Moto G
The following are known to work fine: Nexus 5, Samsung Galaxy S3, Samsung Galaxy S4, Samsung Galaxy S5, Toshiba AT7-C
Feel free to submit your phones to email@example.com so we can continue building a comprehensive list.