Will God forgive if I ask God for forgiveness multiple times or will He punish us?

Thank you for the honest question.
This is a question that we may struggle with when we make mistakes or disappoint God at times and are not sure on how to deal with the guilt of having done it again!

So, What does Bible say about forgiveness? In 1 John 1:9 , it says -“If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness.”. The verse makes it clear that for God to forgive us, we have to genuinely repent and confess our sins and if we do so, He forgives us for sure and there is no doubt about that. That is a promise we can hold on to. The Bible also tells us that "As far as the east is from the west, so far has he removed our transgressions from us”. (Psalm 103:12)
So two things are very clear
1. God will forgive me my sins if I genuinely repent and go back to Him seeking forgiveness.
2. When God forgives my sins, He removes it far from me and does not keep accusing me of those sins again.

Since we are human beings and make mistakes, even after we repent about certain things - it is important for us to understand God's forgiveness in a proper sense, as the saying goes - a Christian may sin less, he is definitely not sinless! No matter in which area we make a mistake, we shouldn't delay going back to God seeking for forgiveness. The devil can play with our mind and feelings and tell us that God will never forgive us and that we have messed up too much. And sometimes, we do mess up really bad and repeat certain mistakes - but that should not make us give up on our walk with God. The devil tries to stop us from going back to God by putting lies into our mind.
In the Bible we see many people going back to God after huge sins - like a Peter who denied Jesus thrice or David who got into an affair with another man's wife. We see that in each case - when they truly repented of their sins, God forgives them.

Having said this - it is also important for us to realise that it is not possible for a true believer to live a constant unholy and unrepentant life. It is highly doubtful that a person who goes on to sin repeatedly simply because he/she thinks that God will always forgive, is a true Christian. Though a Christian may make mistakes - such a person will not continue to live in a sinful lifestyle all the time. A true believer will always do his/her level best to avoid sin and resist sin as the Bible commands(Rom 12:9). Such a person, if he or she makes a mistake will grieve about it and seek for forgiveness from God. They understand how God views sin and will not leave the matter undealt with.
The fact is, no matter what the sin is or how many times you've asked for forgiveness, God will forgive us provided we are truly repentant of our mistakes. So a person who is trying to fool around with God by deliberately sinning and a fake lifestyle will not receive forgiveness as he cannot show true repentance.

When it comes to punishment, a crucial truth we have to grasp is that being forgiven doesn't necessarily mean we will not receive a punishment. Our parents will forgive us and at the same time punish us as a part of disciplining us. King David was forgiven by God after He sought God's forgiveness - but also lost the baby as a punishment.
In Hebrews 12:9-11, we see this "Moreover, we have all had human fathers who disciplined us and we respected them for it. How much more should we submit to the Father of spirits and live! 10 They disciplined us for a little while as they thought best; but God disciplines us for our good, in order that we may share in his holiness. 11 No discipline seems pleasant at the time, but painful. Later on, however, it produces a harvest of righteousness and peace for those who have been trained by it."
Thus God may punish us for our mistakes here on earth simply so that we are changed and shaped to be more like Him as days go by. This is done because He really loves us. But we will not receive the eternal punishment for our sins if we are in Christ Jesus and are children of God. (Romans 8:1)

So, when we fall or make mistakes, don't try to run away from God and hide yourself in guilt - but in humility go back to Him in tears and seek His forgiveness - because as we saw, He is Just and Faithful to forgive us when we do that!