I can confirm that forfeiting challenge if you are not going to beat the villian will stop you from gaining any experience and thus you won't lose out on the feat reward. Not a great option, but I at least felt comfortable enough to play knowing that I had an option to avoid the permanent loss. 

I have a similar Problem: http://imgur.com/a/x6W8g

However I did win my quest!

It was a 6 character party and 4 of those achieved level 20 at the same time. 3 of them got the card feat but the 4th, my Lem didn't receive anything.

I tested playing him up to level 21 and paid close attention to what happens then. The answer is nothing. He leveled. He should have gotten a weapon and the game just didn't move to the reward screen. So apperently this one character is somehow broken for me as all 10 others got their card feat normally on level 20.