This verse contrasts the temporal sufferings brought on by the turning over to Satan with the eternal glory these sufferings may bring in the day of the return of Jesus Christ. I think our problems come because we do not have a full biblical understanding of the key words in the phrase you mentioned - "that the spirit may be saved." Both the word, spirit, and the word, saved, are taken to mean something according to one application of the word. But forcing these definitions into every verse causes many problems.
The most basic meaning of save is to deliver. The most basic meaning of spirit is the unseen nature of something and that which gives life and liveliness to man and beast. Now, there are many applications of these words and they all (as far as I know) fit these general definitions. But they have other very specific applications of meaning as well. Save can refer to the eternal salvation of the believer.
Spirit can refer to the part of man that works with his soul and body to make him a three-in-one being. But every biblical reference to spirit does not refer to this third part of man. Some references simply refer to the inner man as opposed to the seem part of man. This should help you understand the other references which were bothering you: Joshua 5:1; Judges 15:19; 1 Samuel 30:12. This also explains why a beast can have a spirit (Ecclesiastes 3:21).
So, what about our problem passage in 1 Corinthians 5:1? What is the spirit and what does it mean that it is to be saved in the day of the Lord Jesus? I believe that this passage teaches that this man is probably saved, but is committing a horrible sin. Paul recommends that he be turned over to Satan to do to his flesh as he sees fit, so that he will not suffer loss and embarrassment when the Lord Jesus returns; so his inner man (spirit) will be delivered (saved) from loss of rewards at the judgment seat of Christ.
Taken by itself, this verse could readily be used to teach the loss of salvation. It is by comparing scripture with scripture that I know this is not the case here. Our salvation is eternal. Therefore, if this man is saved, he will remain saved. One more thought: Paul may have meant it as a test to see if he was truly saved. The destruction of the flesh would either turn him back to God (and the saving of the spirit) or else it would show him his need for salvation (the saving of the spirit).