It takes a GOOD ... almost fresh quality die and even then ... you need to taper the end of the rod so the die can get a bite. Use plenty of threading lube and go slowly. .
What Deuce said about tapering the end--I just break the 90-degree cut to something near 45 degrees on the bench grinder. Once you get it started, (clamped in a vice!) do the same thing I always do when cutting threads in a hole too--half a turn forward, 1/4-turn backwards, 1/2-turn forward, 1/4-turn back...repeat until threads are the desired length. I've never used cutting out to cut threads in or on anything, and I've never had a problem or broken a tap. I cut threads on a piece of 3/8-stainless for the break rod on my '54 Buick. -Brad
It's actually too soft. It tries to gall in the die. If you don't have a perfectly sharp die and lots of lube, you tear the sharp edge off the threads as you cut them. End up with half the thread you should have.
Whenever I thread a rod its 1/4 turn forward, 1 1/2 turns back once you're onto the rod.Maybe its overkill, but its always worked for me.
I worked in a machine shop for many years and I guess I am old school and old habits die hard. I always use tap and die oil. I even use it on metal if I am cutting with a hack saw ...
The alloy you are trying to thread will make all the difference in how the job turns out. 303 is easier to work than 304. Some of the stainless alloys will harden if they get hot, and cutting threads will produce heat. If you don't know the alloy assume it is 304 which is one of the worst to work with. Stainless is gummy and will not produce chips like mild steel. It is harder to work with. As said taper the end a little and the diameter should be about .005" smaller than 3/8". Use plenty of coolant, I use tapmatic , when threading. Go slow so you don't build heat up in the piece. If you have an adjustable die nut cut the thread a little larger on the first pass and then make a second pass with the proper setting. Make sure that you are centered on the die nut and go straight. If you are off center you will not have an even thread and you will build more heat in the piece on the side with the deeper cut. The die nut has to be very sharp. Back off after each turn to brake the chip. Add more coolant and let the piece cool. The best way to cut threads on stainless is in a lathe or screw machine. Properly set up the chips carry the heat away during the threading operation.
Using a die handle with a guide collar helps a lot. Ace makes one that has an adjustable plate that locks down with three knurl head screws. Making hood steady rods are you?