Coincidental timing of this thread, only a week after a similar one posted to BROL in which the OP there had an epiphany that the rear wheel could lift in hard braking.

Just because you can't tip over at a stop doesn't mean trikes are completely stable in all situations. It sure sounds like you just need to learn how to modulate your braking - those things aren't just on/off, they're also a zillion increments in between. Also remember that you only have brakes on the front of a tadpole. In low-traction situations, braking hard can also cause the trike to go end-for-end, which is also a good way to lose some skin.