Are Christians required to forgive when there is no repentance?

I suppose it depends on which passage of Scripture you're looking at. Here's one that supports that idea:

Jesus said, "If your brother sins, rebuke him, and if he repents, forgive him, and if he sins against you seven times in the day, and turns to you seven times, saying, ‘I repent,’ you must forgive him.” Luke 17:3-4 (ESV)

So, I suppose based on a passage like this an argument could be made for withholding forgiveness when repentance has not been expressed. But, to be fair, there are other passages which speak of extending forgiveness while mentioning nothing of repentance. Check out the two passages below...

Then Peter came up and said to him, “Lord, how often will my brother sin against me, and I forgive him? As many as seven times?” Jesus said to him, “I do not say to you seven times, but seventy-seven times." (Matthew 18:21-22 ESV)

Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you. (Ephesians 4:32 ESV)

When it comes to forgiveness I have a question of my own: Why would you not want to forgive? As believers we come to learn that unforgiveness is not unlike a poison that courses through our hearts, corrupting our thoughts and ultimately leading to bitterness. And bitterness ruins everything — including our relationship with God. (See Hebrews 12:15) So I think it's better to err on the side of seeing forgiveness as a mandate regardless of what the offender does or doesn't do.

But let me be quick to add that real forgiveness is a work of the Holy Spirit. That means if you and I are waiting around for the desire to forgive someone who has hurt us we're in for a long wait. Forgiving others is first and foremost an act of obedience. And secondly, it's just a smart thing to do. If you're struggling with forgiving someone you need to come to God and confess that inability and ask for His grace to forgive.

Does God forgive without repentance?

This is a common follow-up question but I have to be honest that I feel uncomfortable comparing the forgiveness we extend to others with the forgiveness that God offers. The sins and offenses we commit against one another are made by sinners, against sinners. But the sin that is committed against God is a wholly different matter since we are offending One who is perfect in purity and holiness. In other words, it's not comparing apples and apples. The One eternal, almighty God is on a level that is entirely His own when it comes to such things.