I don't know if it's a issue or it designed to work in this way.
Where i live, it's common stay hooked up in a poor connection. I use the premium version and i have downloaded my favorite songs.
And with the poor connection the problems start.
If you have a 1G, 2G the device understands that you have connection and won't play yours offline musics, the app trying play online but it wont work because the poor connection.
This occur even in high speed connection(3G, 4G, WiFi) that reached the limit of the plan, then company cuts your speed to almost zero. Again the app understands that you stay online and didn't play offline songs neither play online, again because the speed of the connection.
In this cases the solution that i encountered was turn off the connection. But its a problem, because some internet plans allows you stay connected in high speeds in some services like WhatsApp or Facebook. And with this i must to choose between stay connect on Facebook and not play songs or play my songs and stay offline on Facebook.