IOS – “iTunes could not connect to this iPhone. This device is no longer connected.”

I have a first generation iPad Air (with up-to-date iOS 8.1)

When I connect it to my 2013 iMac (with up-to-date OS X Yosemite 10.10) – it doesn't work.

Specifically – iTunes automatically launches, but then quickly shows a dialog window that says, "iTunes could not connect to the iPhone. This device is no longer connected."

(That's not a typo – it really says 'iPhone', not 'iPad')

Here's a screenshot:

Meanwhile – on my iPad – in the upper right-hand corner (where the battery life is displayed) – you can see the "plugged in" icon (lightening bolt) rapidly blinking on and off.

In other words – it seems like, when it's plugged in – it's rapidly connecting and disconnecting (several times per second).

If I click "OK" on that dialog window on iTunes – it instantly pops back up, and continues to do so as long as I keep the iPad plugged in.

So – bottom line – I cannot connect my iPad to my iMac.

I'm virtually certain that I was able to connect my iPad before I upgraded to Yosemite on my iMac, and iOS 8 on my iPad.

Thanks in advance for any help!