Try talking to the king again, then return to Grisha. Maybe try Sir Patrick again, as well, if that doesn't help. A few people have had problems with this quest, but talking to those involved several times is generally enough to trigger the stubborn speech option (though more people have had a problem with Sir Patrick getting the breastplate than with Grisha forging it with the gem).
I assume the quest for the breastplate shows up as completed in your questlog?
Dragon Armour Quests