If a Christian finds himself doubting his beliefs and maybe for a while stops believing, is there any way for him to be saved and forgiven? Is it possible for such a person to regain his salvation, or can a period of disbelief never be forgiven by God?

I do not believe that the Bible teaches that a man can lose his salvation. Therefore, it does not have to be regained. However, I will agree with you that a true believer can go through a period of disbelief. He may get his eyes off the Lord and on the things of this world and thereby lose an active faith in the Lord. He may as a result doubt his salvation and even doubt the existence of God. But this does not make him lost.

2 Timothy 2:13If we believe not, yet he abideth faithful: he cannot deny himself.
See All... If we believe not, yet he abideth faithful: he cannot deny himself.

When we get saved, we are united with Christ. We become "members of his body, of his flesh, and of his bones" (Ephesians 5:30For we are members of his body, of his flesh, and of his bones.
See All...) and are "accepted in the beloved" (Ephesians 1:6To the praise of the glory of his grace, wherein he hath made us accepted in the beloved.
See All...); that is, in Jesus Christ. Christ is our life (Colossians 3:4When Christ, who is our life, shall appear, then shall ye also appear with him in glory.
See All...) and we "are complete in him" (Colossians 2:9-10 [9] For in him dwelleth all the fulness of the Godhead bodily. [10] And ye are complete in him, which is the head of all principality and power:
See All...). Therefore, even when we are not faithful to believe in Him, He is still faithful to keep us because for Him to deny us would be to deny Himself.

The answer to a time of unbelief is not to get saved again. Rather, it is a call to renew our faith in the Lord. And, graciously, the scriptures give us the means by which we can do this.

1. We must get into the word of God and meditate on its precepts. Romans 10:17So then faith cometh by hearing, and hearing by the word of God.
   See All... tells us, "So then faith cometh by hearing, and hearing by the word of God."
2. We must spend time in prayer with God. We would do well to fast and pray. Of strong faith, Jesus said that "this kind goeth not out but by prayer and fasting" (Matthew 17:21Howbeit this kind goeth not out but by prayer and fasting.
   See All...).
3. We must be obedient to what we know and understand. Jesus said, "If any man will do his will, he shall know of the doctrine, whether it be of God, or whether I speak of myself" (John 7:17If any man will do his will, he shall know of the doctrine, whether it be of God, or whether I speak of myself.
   See All...). Confidence in the truth of God comes from obeying the truth we already have. If we exercise the faith we have, God will give us more faith. In Mark 9:24And straightway the father of the child cried out, and said with tears, Lord, I believe; help thou mine unbelief.
   See All..., the father of the possessed child cried out, "Lord, I believe; help thou mine unbelief."

If we will come to the Lord as He would have us to, our faith (if it is true faith) can and will be renewed.