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If you want to develop a houserule, then a poll to see if people want to play it that way would be useful.

Warpsolution wrote: Sure, I can see that. But can't you see that the idea of re-rolling a passed and a failed save once each makes sense? Your example breaks the rules I offered up because each "type" of armour save is rolled more than once (and I am pretty sure that there is no way that any two armies could offer up that kind of ridiculousness anyway).

What you want is justification to make multiple rerolls. Reroll only affects the initial roll for (whatever). In the OP it was about Armor Saves. If the initial roll is to make an Armor Save, then Pass or Fail, the Items in the OP can only work on the initial roll.

So no it doesn't "make Sense," as this is a very specific situation that can only occur between two specific armies with specific items that work counter to each other.

Warpsolution wrote: If a die can only be rolled once, then someone could steal all of your dice but one and force you to forfeit the game because "you can't re-roll it". Or maybe I make the same break test eight times, each with a new pair of dice, since I haven't re-rolled any dice. That is obviously silly. So...the definition of "a roll" has got to be in why it's rolled, not the physical die you picked up and tossed down.

True enough, The "Roll" is about the nature, or "why" a die is rolled.

A "Reroll" is only incurred by the Initial Roll Result being affected by an item that has an effect that is triggered by the preset circumstance of the pass/fail result indicated by the Initial Roll Result.

In other words, it is like a flow chart...
An attack hits, roll to wound - roll dice to wound - interpret the result, pass or fail - do any items allow for a reroll based on this result? yes/no?
At this point , if no wound is rolled and no item allows for a reroll this attack ends.
If a wound is rolled and no item allows for a reroll, or if a reroll results in a wound - Roll dice for armor save - interpret the result pass or fail - do any items allow for a reroll based on this result yes/no?

In this example only one wound is discussed. Based on the items in question, regardless of the initial result, a reroll will be made. If the result is opposite of the initial roll result,
and this is where your suggestion runs into problems, you want to roll the armor save yet again in hope it will reverse again and reflect the initial result.

Example:
The armor save is rolled - pass
Attacker item forces a pass to be rerolled - fail
Defender item forces a fail to be rerolled - (whatever, as this result then MUST now be accepted)

Another way to decide this, with a house rule, would be that the items cancel each others effect and are both nullified, neither having any influence over the initial roll result, because that is effectively what you are proposing any way, just with a slight random factor added for suspense.