I think that is the card, it's the Imperial card that reduces deployment costs by 1. Does the discount work per model of the group? For example, does a storm trooper group cost 5 or 3 to deploy a new squad? And if reinforcing a group from 1 to 3, does that reduce the cost of each trooper (2 points total) or just for the group (3 Points total)?

I would believe it to reduce the cost for a group or Deployment card of Troopers by 1.

The exact wording is:

"When you deploy a Trooper , reduce its cost by 1"

And as as I understand the rules for deployment you (the Imperial player" must deploy an entire group/Deployment card.

When the Imperial player "fills up" a partially destroyed unit/group it is called "reinforce"

Does Endless Ranks stack? Ex: I deploy a ST Unit for 5 (6-1) Threat. They die (it's kind of their thing!).

Does that Trooper card 'persist' IE: Is its cost still 5 because I previously reduced it, thus when I redeploy it becomes cost 4?

That would certainly be more in keeping with the card title as saving one threat isn't really going to translate into much more than an extra Trooper every ~6* rounds, and that seems like a very under-powered card for 2 XP.

* (varying with longevity and E-WEB / ST selection)

Edit:

And if it DOES stack, does the effect take place before or after I pay for it? IE: Does the first ST deployment cost 6, while subsequent re-deployments cost 5, 4, 3, etc?

If the RAW said "Troopers cost 1 less threat to deploy" I wouldn't consider this interpretation, but, as written, it sounds like a gradually intensifying effect to facilitate the sending of wave after wave of your own men at the enemy.

It doesn't stack... it's 1 'dollar' off it's base cost each time.

So 5 dollars to deploy... they all die.

5 dollars again to redeploy... they all die.

5 dollars again, etc etc...

But that seems so at odds with its title.

I guess it nets you a free use of combat medic per unit? That's not nothing; perhaps my brain is just trying to reconcile the title with the effect.

Something that speaks to a more subtle logistical advantage would probably have been more appropriate.

"Mass Production" / "Streamlined Logistics" / "Discount Plastoid"