'...If indeed you continue in the faith.' is a phrase in Colossians taken up by those who don't believe in eternal security.
"And you, who once were alienated and hostile in mind, doing evil deeds, he has now reconciled in his body of flesh by his death, in order to present you holy and blameless and above reproach before him, if indeed you continue in the faith, stable and steadfast, not shifting from the hope of the gospel that you heard, which has been proclaimed in all creation under heaven, and of which I, Paul, became a minister." - Colossians 1:21-23 ESV
There is this grand explanation of who Jesus Is and then comes these statements about our past and the word 'if' becomes a stumbling block to English speakers. Are we only reconciled if we continue in the faith? Do we have to be steadfast in order to have salvation? Is this blamelessness Paul is speaking of our responsibility to keep ourselves clean?
No. A thousand times 'no'. Jesus has reconciled us and that reconciliation continues. It is based on who He Is and what He has done. We must hearken further back in the chapter to understand this.
"And so, from the day we heard, we have not ceased to pray for you, asking that you may be filled with the knowledge of his will in all spiritual wisdom and understanding, so as to walk in a manner worthy of the Lord, fully pleasing to him, bearing fruit in every good work and increasing in the knowledge of God. May you be strengthened with all power, according to his glorious might, for all endurance and patience with joy," - Colossians 1:9-11 ESV
This is all one chapter for a reason. Paul knows that these believers are in danger. The danger is that this great finished work salvation will become divorced from their thinking. The danger (among other dangers) is that these people will develop an identity outside of Christ as Christians and not remain people who just believe and receive.
Jesus has done something for us but our old lines of thinking can hinder our knowledge of that reality. Our steadfastness must be in rehearsing the truth and focusing on who Jesus Is and what He has done. It isn't performance. It is recognition and what is at stake is not our salvation it is experiencing our salvation in a real way.
Paul is talking about losing our house keys not losing our house. He doesn't want us to leave our bank card at home because then we won't be able to get to our money. Knowledge of the finished work is like having a cell phone to make the call we scheduled at a certain time. If we don't remain steadfast to bring our wallet, keys and cell phone then we will lapse back into old thinking and we were once 'once were alienated and hostile in mind, doing evil deeds' (see verse 21)
'Don't we have some responsibility to do something?'
The only responsibility we have is to believe in Jesus. That is all we say to people who don't know God and that is all we say to people who do know God... only believe. If we believe and rehearse our belief God will change our desires and it will change the way we walk and what we want to be a part of.
"He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, in whom we have redemption, the forgiveness of sins." - Colossians 1:13-14 ESV
'He has delivered us.' Thank You God. Precious blood bought our pardon. We rehearse 'The Faith' today. We look at you work and marvel at your Son. You sent a Savior to save us and we are set apart because we have received the gift of what happened at the cross. God and man are reconciled. Keep us steadfast in that understanding. We worship You today. You are amazing. We turn our eyes upon Jesus and look into His face... and worship.