I had an iPhone 6+ 128GB that started showing these exact symptoms after upgrading to iOS9. After a Saturday morning of frustrating locking & unlocking and/or rebooting the phone at least 10 times with in 30 minutes, I had called AT&T support (I have AT&T's care package on my phone). They asked me to perform a factory reset, etc. In my opinion, AT&T has had many calls about this, as they were very familiar with my issue. In the end, they told me to contact APPLE support to get addition help and if they could not help me to call them back. So I called APPLE support about my OUT OF WARRANTY iPhone 6+. They wanted me to again to a Factory Reset. This time after the Factory Reset and at the SETUP screen, the touch screen stopped responding "HELLO" prompt. So I had to restart the phone just to setup the phone. APPLE told me it was a HARDWARE issue and wanted me to take it to an APPLE store to have the screen replaced for $150. Well, I called AT&T back, submitted a claim with them and got a Brand New iPhone 6s+ (for $99) as a replacement. After Set Up and Upgrade to iSO 9.1, I restored my phone from my backup. The next morning, I started seeing the same lag/freeze/COMA issue, however on the 6s+ it seem to come out of it's own COMA by itself. It's been 2 days with the iPhone 6s+ and only experienced the FREEZE issue the first morning I had it, but since then, no issue. However, the fact that I experienced the issue on a 6s+ tell me that it's not a hardware issue and that APPLE is not doing this deliberately to anyone that doesn't have an 6s phone, but related more related to iOS9. Of the people I know that have a iPhone 6/6s, they have not seen this issue. Time will only tell if they fix this, however, I read in these forums, that iSO 9.2 was coming out soon and was built for this issue.