The wisdom of Solomon tells us:
Pr 3:5 Trust in the LORD with all thine heart; and lean not unto thine own understanding.
While all the sailors, men highly experienced in the things of the sea, who knew what extreme danger they were in, while all these trembled with fear and had given up all hope, for the things in which they had placed their hope were now gone, while these men feared, along comes Paul and says:
Ac 27:21 But after long abstinence Paul stood forth in the midst of them, and said, Sirs, ye should have hearkened unto me, and not have loosed from Crete, and to have gained this harm and loss.
22 And now I exhort you to be of good cheer: for there shall be no loss of any man's life among you, but of the ship.
23 For there stood by me this night the angel of God, whose I am, and whom I serve,
24 Saying, Fear not, Paul; thou must be brought before Caesar: and, lo, God hath given thee all them that sail with thee.
25 Wherefore, sirs, be of good cheer: for I believe God, that it shall be even as it was told me.
So what makes hope live? Hope is alive when we have the things we trust. The sailors on the ship with Paul felt comfortable at sea because everything was familiar to them. They had their ship, their sails and rigging, the seas and coast lines that they were familiar with. Everything was the way it should be.
At least that was the way it had always been before. Now all these things had to be discarded as not being as valuable as their own lives, but when they had cast overboard the things they placed their trust in, they also cast their very trust overboard with them.
So what can be done to avoid loosing all hope, as these poor sailors did? The solution is to place your hope in something you can never loose, and in something that can never fail you.