There are many scriptures which indicate that once a person is born again according to John chapter 3, they are eternally secure in Christ.

A few of these are:

Heb 13:5-6
"I will never desert you, nor will I ever forsake you, so that we confidently say, ‘The Lord is my helper, I will not be afraid. What shall man do to me?' "
 
John 10:27-30
"My sheep listen to my voice; I know them, and they follow me. I give them eternal life, and they shall never perish; no one can snatch them out of my hand. My Father, who has given them to me, is greater than all; no one can snatch them out of my Father's hand." 

Matt 18:12-14
"What do you think? If a man owns a hundred sheep, and one of them wanders away, will he not leave the ninety-nine on the hills and go to look for the one that wandered off?  And if he finds it, I tell you the truth, he is happier about that one sheep than about the ninety-nine that did not wander off. In the same way your Father in heaven is not willing that any of these little ones should be lost."

Rom 3:28
"For we maintain that a man is justified by faith apart from works of the Law."

Gal 2:16
"..nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, so that we may be justified byfaith in Christ and not by the works of the Law; since by the works of the Law no flesh will be justified."

2 Cor 5:17
"Therefore if anyone is in Christ, he is  a new creature; the old things passed away; behold, new things have come."

There are many problems with believing that one can lose his salvation. What exactly is 'bad enough' to lose your salvation? The book of Romans is very clear that we are not saved by our works, but by faith in Jesus, so the reasoning that we maintain our salvation by good works contradicts the Gospel.

It's also hard to understand how we can be made God's children one day, then we're not, then maybe we are again, especially when we know that God's wrath and judgment is on sinners, but grace and mercy on His children. Does God vacillate between wrath and mercy toward someone who has become His child?

Also, most Christians will agree that all the believer's sins, past, present and future, are covered by the blood of Jesus. Otherwise, we'd be lost if we died with any "unconfessed sin". So if the future sins were covered at conversion, how are they "uncovered" when the believer "falls away"? Was Jesus fooled by the initial conversion?

Also, if God sets His love upon the Christian, but His wrath abides on the sinner, how was His love upon us while saved, but now removed, if we've been "lost again". Does God give and take back His love? How can we become children of God one day, and enjoy God's love, protection and promises, and be rejected by Him the next day? Again, was God "fooled" into thinking we were something we really weren't?

The problem with thinking that you can be saved and then lost again is that God sees the end from the beginning. He can't be fooled or taken in by anything. He knows how long our life will be and what our end will bring. If someone is going to end up lost, it's impossible that God would "save" him "for awhile".  

Many would look at the prodigal son after he had run wild and declare that he had "lost his salvation". But it's clear that the Father always considered him to be his son, even though he was living a sinful life.
 
Galatians 5:19 describes the deeds of the flesh and states that those who are in the flesh and living this kind of lifestyle will not be saved. But Rom 8:9-10 says,

"However, you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. But if anyone does not have the Spirit of Christ, he does not belong to Him. If Christ is in you, though the body is dead because of sin, yet the spirit is alive because of righteousness." 

So again we see that we are saved by God's grace through faith, not by our works. Now it is true that a born again believer will have characteristics consistent with Scripture. They will have a conscience and a desire to please God. Sometimes, people mistakenly believe someone has been born again because of an outward act, when in fact; there has never been a change on the inside.