What dia are the lead bullets?
As Twodog max relates, those made for the 44-40 will usually be slightly smaller in dia than those .44cal bullets for the .44spcl/44mag.
.427/428 vs .429/.430

That was the orig .44-40 groove dia spec. A lot of the modern 44-40 caliber guns just use the larger dia 44cal bbl specs to save bbl production costs.
But the bullet dia you are using AND the dia of the expander in the die set you have can be an issue.

If you have the smaller dia bullets and the die set has an expander for the slightly larger .429/.430 dia 44 projectiles,,that plus the very thin brass will not give you much grip on the bullet.
They will easily be pushed back into the case. Add to it, no crimp or a very light one and the bullet is just barely hanging on in the neck of the brass.

I put a decent roll crimp on my 44-40 reloads, but don't over do it.
Crimp the case so the edge folds over into the crimping groove of the bullet,,sounds crazy to even mention but I've seen some reloads that were simply crimped into the solid portion of the side of the bullet.
Not much holding power in that.

The round needs a pretty good crimp if used in the lever action with a full tube of rounds so the bullets aren't pushed back by simple mag spring tension.

I seat and crimp in one operation, always have and don't have any problems doing so. Many do those as separate trips through the press. What ever works for you.

I load the 44-40 for 2 orig Mod 73 rifles and an orig 92 SRC. Plus a Colt Bisley.
Brass life is as good as any other.
Trying to crimp the round too heavily usually just results in the thin wall of the case crimpling,,not being able to support the force being pushed down and inward on the top edge in the crimping motion.
The crimp groove in the bullet is only so deep anyway. So trying to press that thin brass any deeper than that depth and something has to give,,and it's usually the case wall beneath it.

I use about any headstamp brass I happen to have. It all seems to work OK.
I have found that some 38-40 brass necked up to 44-40 is too thick in the neck.
It necks up OK and sizes fine. Looks just like any other 44-40 case.
But the thicker brass walled necks then bulge when the same bullet is seated. These won't come close to chambering in any of my guns.

Back into the drawer to wait for a 38-40 project to reload for.