There's an incident recorded in the Bible, where a few people tried to cast demons out of a possessed man (Acts 19:13-17). The demons recognized the name of Jesus, but attacked those who used His name, because of their wrong attitude. There is a lesson to be learnt there. The name of Jesus is powerful. When we use His name, we need to have the right attitude. Not a "will this really work" attitude, but a "I've received authority from my Lord Jesus, so obey my command" kind of attitude (Luke 10:19). Let there be no fear in us. God has not given us a spirit of fear but a spirit of power (2 Timothy 1:7)!
When we pray for others, things happen in the invisible spiritual realm. We stand out from others who're not praying. Both angels and demons, who are part of the spiritual realm, are affected by our prayers. Angels - strengthened to do God's will more on this earth. Demons - bound or weakened in their evil work. So naturally we gain some friends and earn some enemies.
We read in Ephesians 6:12 ...
For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms.
Is this a cause for concern? Should we be afraid of this spiritual warfare? Yes, it is right to recognize the impact our prayers create, and give it the due importance. But it is not right to stop praying! Because the following verses say ...

Therefore put on the full armor of God, so that when the day of evil comes, you may be able to stand your ground, and after you have done everything, to stand. Stand firm then, with the belt of truth buckled around your waist, with the breastplate of righteousness in place, and with your feet fitted with the readiness that comes from the gospel of peace. In addition to all this, take up the shield of faith, with which you can extinguish all the flaming arrows of the evil one. Take the helmet of salvation and the sword of the Spirit, which is the word of God.
All the equipment needed for spiritual battle are listed there. We need to check if all our equipment are in battle-ready condition.
What happens if in a moment of weakness, we sin? It is like having a chink in the armour. Is that the end of us? Will we be destroyed? God says "my grace is sufficient for you, in your weakness I'm strong" (2 Corinthians 12:9). We need to recognize our weakness, confess our sins, and get His forgiveness. Immediately the chink is mended, the full protective armour is back in action!
It is God who chose us first and not us who chose Him (John 15:16). He is faithful even though we're unfaithful so many times. It is because of His grace that we're spiritually alive. He knows just how vulnerable we are and gives His grace accordingly. And His mercy is new every morning (Lamentations 3:22,23). Let's go to Him every day, receive that mercy and grace, and fight this battle.
The moment we accepted Jesus as our Lord and Saviour we're marked in the spiritual realm. Jesus becomes our best Friend, and the Devil our worst enemy. The Devil goes about like a lion seeking whom he may devour (I Peter 5:8). But Jesus, the Lion of Judah, is greater than the Devil! Greater is He who is in us than he that is in the world (I John 4:4). Rejoice! We're on the winning side!
If God be for us who can be against us (Romans 8:31)? Let's continue praying for others.