So I don't have a 2014 but I do have a 2015 with the Entune Premium Audio w/Navigation and App Suite. Purchased 11/2014.
My story may not be the same but I thought I would post in case it would help someone out.
I had the AT&T iPhone 5s and everything was working fine with the HU bluetooth and Entune Apps.
Just at the end of April 2016 I upgraded phones and handed down others to the kids. I got the 6s. Bluetooth hooked up no problems but Entune App on the phone would not connect with HU and trying to use any app on the HU would result in message saying I had to have an app running on the phone for it to work.
Created a case with Toyota and took it to the dealer as well. These are all of the things I had tried that did NOT work:
1) deleted all personal data on the HU
2) deleted Entune account through the web-page and built a new one a day later.
3) rebuilt the iPhone 6s without restoring anything as if it was a totally new phone and new account with none of my settings, I only applied the Entune App. Still no Entune synch.
4) took it to dealer where their service tech confirmed I had the latest software on the HU and connected Entune on their own phone successfully but my Entune would still not synch.
5) un-linked all of the associated apps (Slacker, iHeart, Pandora, Movie, Open-table, Facebook) via the web-site.
6) Tried all of the above as well with the USB cable connection.
7) tried all of the above with other iPhones as well including the 5s that I used to have and Entune would not synch for me. I never got around to trying someone with a different phone like an Android.
Keep in mind that in my case bluetooth was still rock-solid and consistently working even after "forgetting" from the phone and vehicle multiple times.
At this point I had resigned myself to just using Bluetooth as all of its functions worked perfectly from the beginning.
The HU and the Entune App on the phone just didn't seem to see each other for my particular Entune account.
I really like the voice feature in the vehicle in terms of searching for a destination and that only works with Entune.
SOMETHING FIXED IT ALL:
Last week there was an Entune App update in the Apple App Store. I downloaded that to the phone but the HU still would not see that Entune was running on the bluetooth connected phone. Nor would the HU see Entune running on the phone if the phone was connected via the USB cable.
Now I don't know which of these two items actually fixed the problem, but here they are:
1) Apple put out an iOS update to 9.3.2 from what I had (9.3.1). iOS 9.3.1 though was on my 5s when it worked properly before.
At this point I should have tried Entune again but I didn't. Instead I opened Entune on the phone and un-linked all of the associated accounts (Slacker, Facebook, Open-table etc.) but this time via the app running on the phone rather than through the website.
2) with no apps signed-in (linked) to Entune I connected the phone to the car and suddenly Entune connected too!
Now the HU displayed that an update was needed and so I let it run and install.
With the update completed on the head unit I shut down the car.
I logged into Entune App on the phone. I went through and linked all of my associated accounts again via the iPhone app (not via the website). Restarted the car and everything linked up again and working.
So I am not sure if the iPhone iOS update was the resolution or me unlinking my accounts via the Entune App on the phone or the combination of both. Maybe if it applies to someone else they can try unlinking the accounts via the app on the phone to see if that gets Entune to synch before applying the iOS update.
