In reading the Puritans, it seems they believed that salvation was a free gift but then a Christian must work hard not to lose their salvation. Is this true?
Unfortunately, we are not experts in Puritan writing, but this is just as well, since Christians are not to search for the truth of our faith in the writings of other men, even other Christian men. Rather, we find such truth in the pages of scripture alone.
On the authority scripture, we can assure you that salvation is not obtained by human works nor do human works "keep" or ensure our salvation. Paul himself rebuked the Galatian church for thinking they could maintain their salvation or become "perfected" by their works:
Gal. 3:1 You foolish Galatians, who has bewitched you, before whose eyes Jesus Christ was publicly portrayed as crucified?
Gal. 3:2 This is the only thing I want to find out from you: did you receive the Spirit by the works of the Law, or by hearing with faith?
Gal. 3:3 Are you so foolish? Having begun by the Spirit, are you now being perfected by the flesh?
Paul calls the Galatians "foolish" for believing that their flesh (i.e., their works) could contribute anything to a salvation that is by grace alone.
Those who believe a Christian can "lose" salvation do not understand the nature of salvation itself. When a man is saved by God's grace, he is given the gift of faith, according to Eph 2:8.
Eph. 2:8 For by grace you have been saved through faith; and that not of yourselves, it is the gift of God;
Eph. 2:9 not as a result of works, so that no one may boast.
God delivers faith to the heart and prompts our confession of faith by means of His Spirit, Paul says:
Gal. 4:6 Because you are sons, God has sent forth the Spirit of His Son into our hearts, crying, “Abba! Father!”
Rom. 8:15 For you have not received a spirit of slavery leading to fear again, but you have received a spirit of adoption as sons by which we cry out, “Abba! Father!”
Once the Spirit of God enters a man, He changes the man's nature forever, making him alive with the indwelling of God's spirit:
Eph. 2:1 And you were dead in your trespasses and sins,
Eph. 2:2 in which you formerly walked according to the course of this world, according to the prince of the power of the air, of the spirit that is now working in the sons of disobedience.
Eph. 2:3 Among them we too all formerly lived in the lusts of our flesh, indulging the desires of the flesh and of the mind, and were by nature children of wrath, even as the rest.
Eph. 2:4 But God, being rich in mercy, because of His great love with which He loved us,
Eph. 2:5 even when we were dead in our transgressions, made us alive together with Christ ( by grace you have been saved),
Eph. 2:6 and raised us up with Him, and seated us with Him in the heavenly places in Christ Jesus,
Eph. 2:7 so that in the ages to come He might show the surpassing riches of His grace in kindness toward us in Christ Jesus.
Paul says this new spirit within us is a permanent part of our being, as a pledge from God that He will complete the work He has begun:
2Cor. 1:21 Now He who establishes us with you in Christ and anointed us is God,
2Cor. 1:22 who also sealed us and gave us the Spirit in our hearts as a pledge.
Phil. 1:6 For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus.
Like a caterpillar becoming a butterfly, a person's nature is changed into something entirely different by the working of the Spirit, and that change can never be reversed. As Paul says:
2Cor. 5:14 For the love of Christ controls us, having concluded this, that one died for all, therefore all died;
2Cor. 5:15 and He died for all, so that they who live might no longer live for themselves, but for Him who died and rose again on their behalf.
2Cor. 5:16 Therefore from now on we recognize no one according to the flesh; even though we have known Christ according to the flesh, yet now we know Him in this way no longer.
2Cor. 5:17 Therefore if anyone is in Christ, he is a new creature; the old things passed away; behold, new things have come.
Notice Paul says the Lord "controls" us and we are no longer recognized (or are known) as someone in the flesh. We are a new creature, like that butterfly that emerges from the cocoon, we can never return to our old nature.
Our salvation is a supernatural, spiritual change, not something obtained nor maintained by the thoughts in our head nor by the works of the flesh, but by the power of God.