I was playing a few matches with my friend with no problems. Then he drafted an arena deck and did a match and the challenge button next to his name remained greyed out on my friendslist, even after he was back in the main menu. He reported that my challenge button was greyed out as well.

The same issue later happened after I did an arena match, with neither of us able to challenge each other.

In both instances restarting the game fixed the issue.