Mud was the biggest reason the French lost. And the armor is not a perfect seal around a knight. Saturate an area with enough arrows and casualties WILL happen. In fact, according to eyewitness accounts the French force still managed to slog through the mud under the shower of literally tens of thousands of arrows while suffering relatively few casualties. It was the longbowmen's ability to actually engage the knights on the muddy ground, plus the use of palings, which turned the day, not to mention a bit of balls by Henry V. Don't blame the armor for keeping them alive, but they WERE exhausted as all hell by the time they engaged, and the broken cavalry charge didn't help matters either.
EDIT: Plus Agincourt was a narrow field with lots of forest around it, so no chance of a flank maneuver.
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