The reason you're having an issue is your using an Apple mobile device. Buying a different Apple mobile device will not help you. The problem you're having seems to be a bug with Apple's player on mobile devices. We're still researching this and waiting to hear back from Apple and some other developer forums we use.
We did find another company that reported the exact same problem on playing playlist on Apple mobile devices on their developer forums, but the issue was never resolved and Apple never responded. Hopefully we will have better luck. If you use a An Apple computer and AirPlay everything will work fine. The problem is only with Apple mobile devices and AirPlay since they use their own player instead of ours.
This is something we're still researching and trying to find answer to or a workaround. We're just in the beginning phase of looking into this and hopefully after the holidays we will know more. But this may be something Apple has to fix on their default mobile player and who knows when or if this will happen. We also hope and think our mobile app we're currently working on will solve the issue since we think we can bypass their default player, but it is premature to say for sure. We're also hopeful that we can get an answer from Apple on a code change or setting we can do that will allow our playlist to pass through continuously and without stopping, but only time will tell. In the meantime if you have an Apple Laptop or computer that you can stream or hook to your TV your problem will go away. Chromecast and Android mobile devices should work fine too.
Is this why I'm also having a problem when I try to use the HDMI adapter instead of AirPlay?