“If God gives us freewill to accept or reject his salvation, will he also allow us by our freewill renounce it and give it back and become lost once again by our unbelief?”.
The Bible answer to your question is no, God does not allow a person who has believed on the death, burial, and resurrection of Jesus Christ for the payment of all their sins, to will themselves out their salvation. Consider John 5:24 where Jesus says, “Verily, verily, I say unto you, he that hearth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.” A person that has believed on Jesus for salvation is a person that is unable to be placed under condemnation again. Jesus also tells us in John 10:27-28, “And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand. My Father, which gave them me, is greater than all; and no man is able to pluck them out of my Father’s hand.” Jesus is saying that a believer is secured in the hands of the Father and cannot be removed (plucked) from those hands, regardless of what they desire. These verses are comforting because we see that God keeps His promises. Our feelings change from day to day. We may feel saved and excited about Heaven one day and then totally different another. Eternal security is not about our free will; it is about God’s promise to never leave us, nor forsake us (Hebrews 13:5).