I get that you can rebuild your deck with cards 2 levels lower than your current adventure.
But it seems unbalanced to rebuild a character with no feats.
So our group decided that you can keep 1 feat per Adventure Deck completed.
So if you die in Adventure Deck 1, then you lose all your feats. But if you die in Adventure Deck 2, you get to keep 1 feat.
We also allow players to regain lost feats by forfeiting the current scenario reward for a feat that was lost due to character death.
So far, we've found this to be a fair and balanced approach.