What kind of flute geometry are you using? I find spiral fluted taps to be weak overall. Also, the extreme positive geometry of the spiral flute tap weakens the tooth form even more.
Its the tips of the tap teeth that are the weakest and first to give up, and its those same dull tips that bind up and jam the tool in the thread being cut.
For really tough going, I would probably grind a serial tap. Remove the tops of the teeth all the way up the tap in such a manner as to retain some relief. (I use a Darex tap sharpening attachment, with eccentric cam motion). This roughing tap should wind in quite readily. Then chase the thread with your finishing tap.
BTW, I have never done this as proof of concept, but it sounds good, don't it?
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)