What denomination believes once a believer falls away they can never be saved?

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That much is certainly true. A better example than Simon is Demas, a disciple of Paul who had Paul fooled for quite a while.

I can't get into the minds of other people, so I can't say that's true. Scripture indicates we should be able to know if we are filled with the Holy Spirit.

Thanks for bringing up Demas. He is a very sad example.

I see a great tension in scripture between those verses which unambiguously state that an individual can have complete assurance of their salvation and verses such as Jeremiah 17:9. If one assumes that this verse applies to unbelievers only, then things fall into line nicely on the assurance side. The problem was that the verse was addressed to God's chosen people, Israel, who, of all people ought to have had a solid assurance of their relationship with God. We know, however, that many, if not most, did not, based on their lives. We also have Matthew 24:24 which is open to interpretation. Can the elect be deceived? In that case, it is not their hearts deceiving them, but false teachers. I think we can all see plenty of examples of professing Christians who were deeply engaged in sound churches, but have been drawn away into cults. Are they saved based on their profession of faith and merely deceived or, like Simon and Demas, were they never believers who, like the seed sown on the rocks, displayed a (false) faith that withered later?