You do not need a preposition after "turn". It simply means "as the days go on..." or "...as the days go by...". When you use "turn in/into/to" it makes no sense. "Turn in/into" has several meanings. 1. to give over as in an exam. 2. to give oneself up, deliver, such as a criminal would turn himself in to the police. 3. to go to bed. Turn into can be used in 2 but not 1 or 3. "to turn to" means 1. to literally turn your body/something toward someone/something. "Julie turned to Simon to ask him a question." 2. to get support from. "John turned to his father for financial help." You can see all the different meanings of "turn" + prepositions at this link http://www.thefreedictionary.com/turn+in As for the meaning of the sentence, it means "others have to accept that their bags are lost and will never be returned to them."

"resign themselves to the fact" and "face the fact" mean almost the same thing. They are both about accepting the current reality of the situation. This is the way I would structure the sentence - As the days go on, others will have to face the fact that their bags are actually lost and they are unlikely to ever see their luggage again.

Hi, I think there's something lacking in your sentence: "...as the days turn INTO WEEKS..." -for example. If it was the case, it would mean that, as time goes by, the probability to retrieve the luggage is lower and lower.