Why?
First, it breaks the "tight math" for AC and attack rolls. Now it's possible for tanky guys to have +x on their armor and a second +x on their shield, but their enemies only get one +x on their attacks. This will make the +/-10 critical rules obsolete on attack rolls. I think this is something the devs are clearly trying to avoid.
I imagine this would make 12th level fighters with the Shield Paragon feat and a +3 heavy shield the ultimate tank with a permanent +25% higher AC than any other front line character.
Second, since shields are meant to be disposable damage sponges that get dented/broken very easily, are you sure you would want broken (destroyed) potency runes? That could get really expensive. Of course, they could just refuse to use Shield Block. Until they're down to their last few HP and Shield Block is the only way to stay in the fight. Then, goodbye expensive potency rune. Or, more likely, "I'd rather die than let my shield get broken because Raise Dead is cheaper than replacing that rune!".
You're welcome. :)
Or the answer is also no as listed on page 379 under shields.
As Seannos says, it isn't allowed by raw. If you did allow it for some reason, you'd need to deal with the questions of does it require resonance, does it impart a bonus to saving throws, etc. If it does, does it only get the bonus when the shield is considered raised? What happens when the shield gets broken, or even destroyed?
Almost certainly, you wouldn't want to allow it to allow it to stack with an armor potency rune. While in a homebrew world, I'm not certain I would prohibit it from being able to be done. (might even consider adding the rune potency to the hardness) But I wouldn't let it stack with an potency rune on the armor.
General gist, I would end up making it likely that most people would put them on the armor and not on the shield. But perhaps someone who typically fought with a shield but otherwise unarmored, for some reason/style might actually choose to have a potency rune on a shield, and might get some actual benefit not unlike being on armor from it.
No you cannot add an armor potency rune to shields. You can add a weapon potency rune to Shield Boss or Shield Spikes though.