Hi Nat82, not sure if you found a solution but I've been experiencing a very similar, if not the same occurrence. I have an iPhone 6S with MBA 11" and for the past 9 months I will intermittently experience the rapid connect/disconnect when plugging the phone into the laptop for sync'ing. I tried rebooting, upgrading to the latest OS's (macOS 10.12.1 + iOS 10.1.1), changing settings in iTunes (disable sync over WiFi, disable auto-sync, delete config files, etc.) and a variety of other options.
My solution - disable WiFi on the iPhone before plugging into the laptop.
I think the problem is iTunes was confused if it should sync over WiFi or cable when plugged in and as a result cause the rapid and recurring connect/disconnect. When disabling the WiFi on the iPhone it doesn't give iTunes the opportunity to get confused since it's can't find the iPhone on the network and as a result, successfully connects when plugged in. After disabling WiFi on the iPhone I also check to see if iTunes was in the middle of syncing or recognized the phone and if so, either try to 'eject' the phone from iTunes or simply close iTunes before plugging in the phone.
Although slightly annoying, disabling WiFi before plugging into the laptop has worked every time and I no longer experience the connect/disconnect issue.
Hopefully this works for you too!
