But you *really* should keep feeding according to the revolution of the spindle on the index until it stops -- so your machine knows where the tap is when it starts in reverse.
The typical tapping head has a special chuck. It uses two ways to hold the tap. A Jacobs Rubberflex type collet to assure concentricity and a pair of plates with a combination left and right hand threaded leadscrew connecting them to clamp down on the flats on the end of the tap shank.
Some floating tap holders have similar chucks.
The main thing to consider is -- if it *does* slip and you are doing rigid tapping, it will no longer be at the right depth for the number of turns which the tap has taken.
I would look for something with the Jacobs tap chuck for this, myself. And the Procunier or TapMatic tapping heads have them, along with other features which make machine tapping easier -- including automatic reversing when you start to back out of the hole -- while the spindle is still turning clockwise. :-)
When doing tapping with a releasing tap holder in the bed turret of my manual lathe, I've made tap holders which are simply the right diameter for the shank of the tap, and a pair of setscrews opposite each other to clamp on two opposing flats.
Good luck, DoN.