There are two extremes with the issue of losing your salvation. One position is that once one accept Christ, losing his or her salvation is not possible. The other position is that one moves in and out of salvation. I guess that anyone who believes this has to hope and pray that he dies on the right day!
This page shows what Scripture really teaches on this issue.
Nobody Else Can Take Your Salvation From You
But Losing Your Salvation Is Possible By Giving It Up
A Delibrate, In Your Face Sin
For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. He that despised Moses' law died without mercy under two or three witnesses: Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace? For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people. It is a fearful thing to fall into the hands of the living God. (Hebrews 10:26-31)
Old Testament Passage
And if any soul sin through ignorance, then he shall bring a she goat of the first year for a sin offering. And the priest shall make an atonement for the soul that sinneth ignorantly, when he sinneth by ignorance before the LORD, to make an atonement for him; and it shall be forgiven him. Ye shall have one law for him that sinneth through ignorance, both for him that is born among the children of Israel, and for the stranger that sojourneth among them. But the soul that doeth ought presumptuously, whether he be born in the land, or a stranger, the same reproacheth the LORD; and that soul shall be cut off from among his people. Because he hath despised the word of the LORD, and hath broken his commandment, that soul shall utterly be cut off; his iniquity shall be upon him. (Numbers 15:27-31)
And let us consider one another to provoke unto love and to good works: Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching. (Hebrews 10:24-25)
But call to remembrance the former days, in which, after ye were illuminated, ye endured a great fight of afflictions; Partly, whilst ye were made a gazingstock both by reproaches and afflictions; and partly, whilst ye became companions of them that were so used. For ye had compassion of me in my bonds, and took joyfully the spoiling of your goods, knowing in yourselves that ye have in heaven a better and an enduring substance. Cast not away therefore your confidence, which hath great recompence of reward. (Hebrews 10:32-25)
No Longer Believing in Christ
Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace. (Galatians 5:4)
For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches. And if some of the branches be broken off, and thou, being a wild olive tree, wert graffed in among them, and with them partakest of the root and fatness of the olive tree; Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee. Thou wilt say then, The branches were broken off, that I might be graffed in. Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear: For if God spared not the natural branches, take heed lest he also spare not thee. Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off. And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again. For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree? (Romans 11:16-24)
An example of losing your salvation according to the Romans 11:16-24 passage would be that should one convert from Christianity to Islam, God would then judge him as a Muslim; and, like all Muslims, he would end up in hell. This passage also states that, should one convert to Islam, he can convert back to Christianity; God would then judge him as a Christian; and he would end up in heaven.
Also, since God gave us free will (see my page on free will vs. predestination), we do not lose our free will once we accept Christ and become Christians.
You Do Not Move In and Out of Salvation
And this is the record, that God hath given to us eternal life, and this life is in his Son. He that hath the Son hath life; and he that hath not the Son of God hath not life. These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God. (1 John 5:11-13)
This passage shows that one can know that he are saved. If one moves in and out of salvation (i.e. one is saved today, but lost tomorrow, and saved again the next day), how could anyone possibly know whether he is saved?
Many churches that teach this teach either that one are saved by grace + works or that one are saved by grace but kept by works. Works do not enter into whether or not one are saved. Please see how to go to heaven for more information.
Therefore, no need to lose any sleep over this!
 All scripture references are from the King James Version unless otherwise noted. Please see my about page for why I chose this translation.