Paul uses the word save (sōzō) nine times in 1 Corinthians (1:18, 21; 3:15; 5:5; 7:16 twice; 9:22; 10:33; 15:2). He does not use the noun salvation (sōtēria) at all in the epistle.

Commentators are not in agreement as to what save means in 3:15; 5:5; and 15:2. I believe, along with some commentators, that in those three verses Paul is talking about being spiritually healthy at the Bema, the Judgment Seat of Christ.  

1 Corinthians 3:15. Many think that Paul is saying that no matter what amount of a believer’s works are burned up, he will be saved from eternal condemnation when his works are judged. (Of course, many would qualify this by saying that it is only true of genuine believers. Many would say that if too many works were burned up, it would prove that the person was not born again in the first place.) There are huge problems with this view. First, believers have already been saved from eternal condemnation, as Paul makes clear in Acts 16:31; Gal 2:16; Eph 2:5, 8-9; and 1 Tim 1:16. Second, salvation from eternal condemnation is apart from works (Eph 2:9). Third, the context of 1 Cor 3:5-15 is the Bema. No one will gain everlasting life there. The issue will be rewards for work done.  

The word sōzō is often used in the NT to refer to being healthy (e.g., Matt 9:22; Mark 10:52; Luke 18:42).  

What Paul is saying is that wise master builders such as himself and Apollos will be spiritually healthy at the Bema, no matter how many of their works might be burned up because they lacked eternal value (e.g., hunting, fishing, golfing, and watching sports are all wood, hay, and straw because they lack eternal value).  

In The Grace New Testament Commentary, Dwight Hunt wrote:  

Paul and Apollos, the examples under consideration (vv 5, 6, 9, 10), were both spiritual men who, if they continued on the same path, would be found healthy at the Bēma, though both would surely have some works that failed to pass the test of eternal value (p. 721).  

1 Corinthians 5:5. This verse has puzzled many, since the issue is church discipline of believers. Paul delivered a believer over to Satan for the destruction of his flesh in order that his spirit might be saved in the day of the Lord Jesus. Many commentators think Paul was saying that if one fails to persevere, he will not win what they call final salvation. This understanding is impossible considering Paul’s many faith-alone statements (e.g., Rom 4:4; Gal 2:16; Eph 2:8-9).

As in 1 Cor 3:15, the issue is being spiritually healthy at the Bema. It should be noted that “the day of the Lord Jesus” confirms this interpretation since in the NT that phrase refers specifically to the Bema. See this article for more details.  

1 Corinthians 15:2. Many commentators have interpreted the word save in this verse to refer to salvation from eternal condemnation because Paul uses the word gospel in v 1, and he refers to Jesus’ death, burial, resurrection, and post-resurrection appearances in vv 3-11. However, that view is impossible for two reasons. First, Paul uses a present passive of sōzō here—meaning is being saved—rather than a perfect tense, which would mean has been saved, as in Eph 2:8. Second, Paul says that this salvation can be lost if one does not hold fast to the word that Paul preached.  

Fee expresses a popular understanding: 

…their very existence as believers is at stake on this matter. That is, any deviation from this gospel which “saved them” and “in which they stand” puts them in danger of “believing for naught (1 Corinthians, p. 718).  

Fitzmyer does, too: 

…you are already in the process of salvation, which is not yet complete; recall 1:18, 21. The gospel is not merely something proclaimed in the past, but it also has present soteriological importance. The third relative clause looks to the future, as Paul links to the gospel “salvation,” which is an effect of the Christ-event that still has to come to its full implementation (1 Corinthians, pp. 544-45). 

Pratt expresses an old-line Calvinist spin: 

Yet, Paul added an important qualification. They are saved, if they hold firmly to the word. As he indicated throughout this epistle, Paul believed that saving faith would set itself apart from insincerity through time. True believers persevere in their commitments to Christ. Paul did not mean that truly regenerated people could lose their salvation, nor that truly regenerated people were without sin and failure. He understood, as the entire Bible teaches, that saving faith proves itself over a lifetime (1-2 Corinthians, p. 258).  

Lowery, however, correctly sees this as a sanctification issue: 

As the former message was an essential element in the Corinthians’ experience of ongoing salvation (the pres. tense of the verb saved focuses on sanctification), so was the latter. To reject bodily resurrection eviscerated “the gospel” and made faith vain (eikē, “without cause” or “without success”; cf. vv. 14, 17) because it had an unworthy object (cf. 15:13, 17). Believing the gospel includes holding firmly to belief in Christ’s resurrection. Unless one holds firmly, his belief is “in vain”; cf. Matt. 13:18–22) (BKC, p. 542).  

Likewise, Hunt writes: 

This statement stresses the fact that the gospel includes more than justification, which brings forth eternal life; it also includes a daily sanctification (are saved) if believers hold fast (or abide in) the word (cf. John 8:31–32; Rom 1:15; 10:9; 1 Cor 15:2; Gal 2:20; Eph 2:10; Jas 1:21). This daily sanctification process relates to the quality of life the Christian will spend in eternity (3:9–15; Luke 19:11–27; Rom 8:16–17; 2 Pet 1:10–11) (GNTC, p. 758). 

Paul uses sōzō in 1 Corinthians 3:15, 5:5, and 15:2 to refer to being spiritually healthy at the Bema. I believe he does, as well, in 1 Cor 1:18, 21, but that is beyond the scope of this blog. I urge you to study the word save in 1 Corinthians and draw your own conclusions.  

Keep grace in focus and you will remain spiritually healthy.