Is it possible for someone to believe for a time and then fall away? Yes, but as Calvin notes, the scripture teaches that those who had this ‘temporary faith’ were not born again:
According to Luke, Christ says that they believe for a time; because that honor which they render to the Gospel resembles faith. At the same time we ought to learn, that they are not truly regenerated by the incorruptible seed, which never fadeth, as Peter tells us, (1 Peter 1:4) for he says that these words of Isaiah, The word of God endureth for ever, (Isaiah 40:8; 1 Peter 1:25) are fulfilled in the hearts of believers, in whom the truth of God, once fixed, never passes away, but retains its vigor to the end. Still, those persons who take delight in the word of God, and cherish some reverence for it, do in some manner believe; for they are widely different from unbelievers, who give no credit to God when he speaks, or who reject his word. In a word, let us learn that none are partakers of true faith, except those who are scaled with the Spirit of adoption, and who sincerely call on God as their Father; and as that Spirit is never extinguished, so it is impossible that the faith, which he has once engraven on the hearts of the godly, shall pass away or be destroyed.
Harmony of the Gospels, Volume II (speaking here of the parable of the sower)