My kill rate went up immensely as I got more comfortable doing shallow insertions.
The hair anchor system and the signaling stem cells are both located at the bulge area, which has a shallow depth and much smaller range of movement than the bulb. If you don't sufficiently heat the structures in that area, then the hair will not release properly and it will definitely regrow.
See the image here: http://www.jci.org/articles/view/27490/files/JCI0627490.f1/medium
Be very careful when doing shallow insertions though, practice making your insertions more and more shallow very slowly until you learn the right depth and energy (most hairs will release cleanly in a single pulse once you get it). Be aware that insertion angle is extremely important on shallow insertions, you *do not* want to fry the sebaceous gland area next to/above the bulge as that is likely to result in pitting.
Also note that it can be very difficult to gauge the proper insertion angle on some curved/distorted follicles (which may be the case on your face if you have a history of plucking), in cases of severely distorted follicles it is better to use blend method or galvanic.