Conditional Security, by nature, is a very ambiguous position to hold. If you believe, as the Bible says, that salvation is by faith alone, then realistically, the only way to lose salvation is to lose your faith. But most believers in Conditional Security hold other beliefs, bringing them dangerously close to works-based "gospels", while remaining ambiguous enough to just barely avoid it.
Conditional and Eternal Security do have common ground when it comes to faith. We both believe that those who do not endure to the end will not be saved, whereas those who do will. The question then becomes can a Christian lose faith? Scripture seems to rule this out as a possibility. It draws a contrast between "those who draw back to perdition" and "those who believe to the saving of the soul" (Hebrews 10:39).
If there was any doubt left after that, 1 John 2:19 tells us "They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us." From this, we see that while it is possible to apostatise, those who do so do not lose salvation, but never had it. Just as Judas was an Apostle, yet was a devil whose condemnation was written about long ago, so also is false conversion possible to this very day. And God knows the heart better than even the false convert themselves.
Do we believe that these false converts would be saved if they died before their apostasy? If so, then how can we judge even those within the Church? Not that this is our place, but are we not called to rebuke false teachers? To mark those who cause division and have nothing to do with them? To not bear with false brethren even for an hour? The Bible is replete with warnings that there are false brethren everywhere. Wolves in sheep's clothing. Not only are we told to spot them, but also to deal with them accordingly. So we must be able to say, even if it means occasionally making the wrong call, that yes, it is entirely possible to say "I am a Christian", yet not be saved. As James tells us, even demons believe, and tremble (James 2:19).
So it seems obvious that while the only way to lose salvation is to lose the faith that brings it, those who lose faith did not have faith that brings salvation, and so they never had salvation to lose. But what of those who do? Can we lose salvation by any other means? "Yes, in a few ways". Well, what are they? "We don't know, it's best to just not test it". You don't think God would tell us this? His word, which fully equips us to be complete men of God (2 Timothy 3:16-17), doesn't tell us "oh by the way, you do this, you go to Hell regardless of your faith"?
The sheer ambiguity of Conditional Security, especially in contrast with the clarity and simplicity of Eternal Security, is enough to mark it as false. If you could lose your salvation, the Bible would not only tell us that you can, but how you can. Instead, it is flooded with endless promises and assurances, from the God who calls things which are not as if they are (Romans 4:17), that we who believe have eternal life (1 John 5:13), and that because no one is greater than the Father, nothing can take us from His hands (John 10:27-29). It takes sheer arrogance to believe you could be the exception.