I think there is a simple solution as to why believers can't agree on this and that is because the Biblical authors don't agree with one another on this. Let's take a comment from the author of the letter to the Hebrews ...
"4 For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit, 5 and have tasted the good word of God and the powers of the age to come, 6 if they fall away, to renew them again to repentance, since they crucify again for themselves the Son of God, and put Him to an open shame."
Hebrews 6:4-6
The author is saying that someone can't be brought back to repentance if they fall away which is to state that someone cannot be brought to a point of repentance if they have repented before and have since fallen away. He even goes on to say that some of these have "become partakers of the Holy Spirit". So say that the author is not referring to believers that he considers genuine would involve reading huge amounts into the text that simply isn't there ... and only to stop Biblical authors disagreeing with one another. Something which doesn't form any part of any standard historical analysis.
If a true believer can't fall away then why issue a warning on something that can't happen? It would be like me saying, "You can't heal the broken leg of a person who has crashed to the ground after flying just by flapping their arms". Well, thanks for pointing that out Emuse! I don't expect I will need to do that any time soon. On the other hand, if a person can have repented, partaken of the Holy Spirit and so on and still not be a genuine believer ... then what?
The simplest solution is that the Biblical authors disagreed with one another on this topic. And why would we even deny that when we know that division arose in the Church early on and in relation to doctrinal issues? What would we make of someone in 2000 years time who took books from Plantinga, Craig and Swinbourne and simply on the basis of an assumption (these blokes were divinely inspired) tried to make them agree with one another? Modern believers can disagree so why not ancient ones? In short, some thought that a genuine believer could be lost whilst others didn't and this is reflected in their writings.
I really don't know what's the issue here? Judas was a believer - the Holy Spirit worked through him when casting out demons, baptizing and the such, - yet he did fall away from Grace. Similarly with Peter - he just went to deny Christ three times(but in his case he didn't go to conclusively deny Christ, but repented and came back to Him).
So, it is within the very text of the Bible how one of the main characters actually was a follower and a believer, but eventually fell away.
This is a perfect parallel to OT covenant - the seed of Abraham was blessed and under Grace, through Abraham's righteousness, due to being descendants of Abaraham. Some of them, although in the covenant with God, sinned and through their iniquities they were expelled from the covenant.
That same thing is going on here. The difference being that Christians accept Christ, thus enter the covenant at this point ; while ethnic Jews were born in the covenant, but expelled themselves by rejecting God. However, in both covenants people DID fall away, once they entered.
The Book of Revelation clearly portrays certain Christ condemning some of the Churches, or if not at least some of the members, although they at some point(at the founding of the Church) did accept Christ and did ENTER THE COVENANT.
So, you can experience the Holy Spirit and eventually fall into wickedness - Judas and some members of the early Church(in Revelation) are the NT example ; while some members of Jewish society did so in OT, by falling into idolatry(though, they didn't lose the Holy Spirit, because it wasn't part of the OT covenant, however they lost the blessings of the Covenant and the saving power of the covenant).
