Notice the direction of the verb. Paul does not tell them to work up more hope. He asks that the God of hope would fill them with it.
That matters, because most of us treat hope as a mood we are responsible for maintaining. When it drops we assume we have failed at something, so we try to talk ourselves back up, and talking yourself up works for about an afternoon.
Scripture treats hope as something handed to you. It arrives from outside, which is precisely why it can survive a week where nothing improved. You are not the source, so you running low does not empty the supply.
The phrase attached to it is worth sitting with too: as you believe in Him. Not as you believe hard enough, or believe without wobbling. Just as you keep turning toward the Person rather than the outcome.
If you are short today, you are not disqualified from asking. Short is the normal condition of people who need filling.
