The title says it all. Eternal flask has a 10 minute cooldown. It should be changed from a hard 10 minutes to also reset when you exit an adventure, like just about everything else.
the difference between the flasks and a one-use clicky is that the clickies cannot be reused before shrining/quest completion, unlike the flasks.
Upside of flasks is their continued use. Downside is they do not reset upon shrining and quest completion.
If they have them reset, we are getting the best of both worlds.
Here is a different suggestion: have their effects endure post-shrining and post-quest completion, right into the next wilderness, quest, etc. We have this tech already in Yugo pots and I think the alchemical potions, and anyway in xp pots. Would that be preferable? Just would be annoying to keep clicking them every ten minutes or so.