So, it's quite known that bishops wore miter over helmets during the 13th century, and I think I remember some references from the 14th century as well. Pretty much, if not all of them, on heaumes. Bishops don't stop fighting there: in the battle of Braxton (1513), also called the battle of Flodden Field, at least one Scottish archbishop is recorded perishing at the battlefield, and I hardly think English ones were much different (specially the lord bishops of Durham). At Agincourt (1415) one French archbishop is recorded being captured by the English, and the bishops of Toledo and Coimbra fought at Toro (1476).

My question is: when the Mitre stopped being used with armor, and why? Did the bishops changed their identification with something else? Or they simply became indistinguishable to other men-at-arms?

I know at least one artistic evidence showing a Pope with the triple papal tiara above an armet, in a church afresco at Apulia, Italy. Boris Gauda dated it 1410:

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Maybe you also need to ask the parallel question: were mitres or mitre-shaped crests actually worn to identify bishops on the battlefield, or was it just an artistic convention? To be honest, I haven't really seen strong evidence either way on this matter.