Hope springs eternal

Нope springs eternal (People will keep on hoping, no matter what the odds.) ≅ Надежда умирает последней.

Example: I keep buying lottery tickets—hope springs eternal.

This expression was coined by Alexander Pope (An Essay on Man, 1732) and quickly became proverbial. (The American Heritage® Dictionary of Idioms by Christine Ammer)

см.
[надежда умирает последней]
[hope against hope]