QuickTime Player disconnects iPhone trying to capture screen

I'm trying to capture my iPhone 5 screen with QuickTime Player, but it's being disconnected. It goes like this:

I have a late 2013 macbook pro with MacOS X 10.11.1. I have an iPhone 5 with iOS 9.1. On the iPhone, I have Trusted the laptop.

I connect the two with a iPhone-to-USB cable, and see that the iPhone battery-indicator shows charging (it's at about 90%)

...On the laptop, Photos automatically launches, showing my iPhone Pictures, but I ignore it.

On the laptop, I launch QuickTime Player and choose New Movie Recording.

..It shows a moving of me, being taken with my laptop camera (if you're trying to duplicate these steps, please note that it will show a movie of you, not me).

I click on the triangle next to the recording button and my phone's name is on there, so I select it.

..At that instant, the New Movie window goes black, my iPhone battery indicator goes back to 'disconnected mode', and then after a little time the New Movie window gets very small and an error sheet appears with "The operation cannot be completed".

...I also notice that the Photos app window, which was showing my iPhone photos, is now showing a generic home screen.

...it appears that trying to capture my iPhone screen is causing it to disconnect from the mac.

Console.log shows:

11/11/15 2:50:33.000 PM kernel[0]: vmioplug: Warning: com_vmware_kext_UsbPortArbiter_12_1_19[9c06f]::updateDeviceByPort(14200000) resetDevice() failed: e00002bc

11/11/15 2:50:34.000 PM kernel[0]: 029555.161004 iPhone@14200000: AppleUSBDevice::waitForInterfacesGated: timeout waiting for _interfacesMatched

11/11/15 2:50:34.000 PM kernel[0]: 029555.161020 iPhone@14200000: AppleUSBDevice::waitForInterfacesGated: timeout waiting for _interfacesMatched

11/11/15 2:50:38.804 PM com.apple.usbmuxd[8339]: USBDeviceOpen failed: 0xe00002c5

11/11/15 2:50:43.871 PM com.apple.usbmuxd[8339]: USBDeviceOpen failed: 0xe00002c5

11/11/15 2:50:48.871 PM com.apple.usbmuxd[8339]: USBDeviceOpen failed: 0xe00002c5

This sort of worked a few times yesterday and the day before, but it was very flaky.

I've tried both USB ports on my mac, and several different iPhone/USB cables. I tried turning the iPhone connector the other way. I rebooted both iPhone and mac. This still happens.

I can't find anything on the interwebs that points to a solution.

Can someone help me?

Thanks,

Robo