Very good idea, Nash, hereby seconded. There is a major difference between challenging them for another PvP Duel "against a friend" and Rematching. PvP 1/2 is not only played for fun but for electrum and cards. If you lose a game thinking "Oh man, my deck would have been such a good counter to theirs and I got that unlucky draw" and have the Rematch button available, you'll simply press it. If your opponent goes like "w00t, I've defeated this expert player, let's do it again", they'll press it as well and you'll have the chance showing off your deck against each other again. The second match will be played immediately after, players won't be able to change their decks. In the end, you'll have made up or doubled your 30/50
loss depending on whether your judgement turns out to be right.
The only exploit I can imagine is a veteran player putting together a farm deck, not minding the electrum loss and giving away shards to a lucky novice by repeatedly playing (letting his AI play?) them. But this can be prevented by offering no Rematch after one player has won the second time, best-of-three-like.
Maybe my take is a bit different than yours; I just spotted that you mentioned "PvP duel" in your OP, do you mean the one without gaining rewards?