In my case, the problem was the temperature of the charger. Since it's currently winter in the southern hemisphere, removing the MacBook from charge causes the charger to cool down (since it apparently draws very little mains power when there is no load on the MacBook side). At some point when it is cool enough, it will refuse to supply power when the MacBook is plugged in again.
The workaround is to warm up the charger (for example, by sitting on it) for a few minutes until the charge light comes on. Then the current running through the charger is enough to keep it warm, and it continues charging.
Update: A year later, after returning from being away for six weeks, my charger refused to work again even after sitting on it. Apple was happy to replace it under AppleCare.
Nope. The iDevice charger has a very limited power output that would be insufficent for running the macbook, let alone charging it.
Going the other way around, however, is a little more doable, an adaptor could be made, but at that point you may as well just plug your iDevice into your macbook's usb port and be done with it.
Best Answer
The chargers have different capacities.
So the ipad charger can charge the pro when it is idle but cannot meet the demand when the pro is working hard.