This is, obviously, a very important question. Perhaps that is why it has been debated so many times and for so long. At this point, it seems most people have made up their mind one way or the other. My goal in attempting to answer this question is to help people think it through in a fresh way.
It is often said that Arminians (a label given to Wesleyans and others who, knowingly or not, agree with a man named Jacob Arminius over and against a man named John Calvin) believe you can ‘lose’ your salvation. I want to suggest that this way of saying it is quite absurd. I ‘lose’ things all the time (my wallet, my keys, etc.). Every time I lose something it is accidental. It isn’t a willful choice to lose something. In this sense, is it possible to ‘lose’ your salvation? Absolutely not!
But what if we worded the question a little differently? Is it possible to ‘reject’ your salvation? All Christians agree that salvation comes through Jesus Christ. But does it come through some sort of irrevocable contract with Jesus or does it come through a loving relationship with Jesus? I think it’s the latter. We are saved by having a right relationship with Jesus. Good relationships, by their very nature, involve at least two willing parties. Could someone enter into a relationship with Jesus and then reject that relationship? I can't imagine doing so myself, but amidst temptation, deception, and persecution it is possible.
It seems to me that all of Scripture implies the possibility of apostasy (rejection of salvation). A lot of the New Testament is written to encourage young Christians to keep the faith (sort of needless if it’s not possible to forsake the faith). I’d be glad to go through the main texts that are sometimes used to prove either side of this debate, but for this post I’ll simply say that a lot of the New Testament doesn’t even make sense if it’s absolutely impossible to turn from the faith.
That being said, I don’t think it is common for people to reject their salvation. I tend to think it is extremely rare. A lot of people that we might suspect ‘lost’ their salvation were possibly never truly saved in the first place. Just because someone prayed a prayer or raised a hand at some point doesn’t guarantee that they actually entered into a relationship with Christ. And just because someone isn’t in a good spot in their relationship with Christ right now doesn’t mean they’ve completely rejected that relationship.
To sum up my thoughts on this matter, I’ll ask the question yet another way. Do I believe that I’m ‘eternally secure’? Yes, I do. I am eternally secure in Jesus Christ. As long as I stay in right relationship with Jesus I am secure. If I’m not in right relationship with Jesus I have no reason to feel secure. If you want assurance of your salvation, stick close to Jesus today. Ultimately, our trust should not be in some past prayer that we prayed to get saved, but in our present relationship with the Savior.