yes it is possible to be in a state where you cannot be forgiven and logically if you cannot be forgiven then you cannot be saved. Jesus said that.
"All sins will be forgiven the sons of men , those who blaspheme against the Father will be forgiven, even those who blaspheme against the Son or the Christ will be forgiven but those who blaspheme against the Holy Spirit will not be forgiven".
If you cannot be forgiven blasphemy against the Holy Spirit then you are irredeemable because of the doctrine that
"MANY are CALLED but FEW are CHOSEN"Blaspheming against the Holy Spirit makes one guilty of an eternal sin
There is a reason why Jesus asked Christians to pray for forgiveness of their sins in the Lord's prayer because it is impossible in the human state to not sin with free will. The Bible encourages repentance and encourages Christians to pray for forgiveness of their sins from God. I do not think Christians who are saved are capable of blasphemy against the Holy Spirit which is the only thing that can make one guilty of an eternal sin so no there is no other sin or thing that can make a Christian irredeemable.