Falling Away & Repentance

Here is a topic we discussed at Bible Study Sunday night ...
Can an immersed believer (baptized) who has fallen away (turning their back on God) be brought back to repentance?

Here is a piece of scripture I feel answers that question:
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Hebrews 6: 4-6

It is impossible for those who have once been enlightened, who have tasted the heavenly gift, who have shared in the Holy Spirit, who have tasted the goodness of the word of God and the powers of the coming age, if they fall away, to be brought back to repentance, because to their loss they are crucifying the Son of God all over again and subjecting him to public disgrace.
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For me, I think the key to the text is where the person is in their walk with the Lord before they "fall away" .... to have been enlightened, have shared in the Holy Spirit and have tasted the goodness of the word of God and the powers of the coming age ... wouldn't that person have to have reached repentance but for some reason at some point decided to turn against God, Jesus and the Holy Spirit? According to this scripture, it's impossible to be brought back to repentance.

Sure glad I'm not the one to decide & I never want to be that person who has 'fallen away'!