Is blessing a whip permanent?

Using a whip to collect a relic with rarity equal or greater to the rarity of the whip will bless the whip, which means that the whip no longer has any drawbacks. I originally assumed a whip would only remain blessed for a single run, but after having died (multiple times) in temples with blessed whips, they retained their blessed status. However, I've only tested this with the uncommon green whips (since I haven't actually blessed any higher rarity whips yet), and higher rarity whips may behave differently than the lowest rarity whip. Plus I'm also wondering if a whips blessed status only lasts a set number of temple runs.

Do whips maintain their blessed status permanently?

It's permanent.

Using the whip to get a relic of the same or higher level doesn't bless the whip but instead, removes the curse. You can see many guides mentioning this curse, like here or here, and it's also mentioned in the Steam page in "About this game" section :

Unlock new whips with success and choose from your collection before venturing into your next run. Each whips carries a minor blessing but also a curse that may complicate your attempt at riches and glory.

Once the curse is removed, it'll never come back, as supported by this Reddit thread talking about a possible way to play again with cursed effect once they're removed.