I don't use an iphone when listening off line but I do have an ipod touch that I take offline when I am connected to my car stereo.
Try these few things:
1. When you are in online mode (and prefably on Wi-Fi), go to the "Your Music" Tab on the homescreen.
2 Select the Playlist you want to listen to offline and hit the switch that says "Available Offline" at the top (it should turn green as in the pic below).
If all is working properly, the songs should begin to download providing you have enough memory. You should see a green arrow next to each song. This indicates the song is now downloaded and stored in your phones memory for offline listening. This can take a while if it's your 1st time depending on the your internet connection and how big your playlist is.
*You do not need to turn your overall setting for Spotify to offline mode. So long as the playlist you want says "available offline" the music will (and should work whether you have an active connection or not.
Let me know if that works.
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