Why does God continue to let Satan exist?

There is a reason. 

As God told Moses to say to the wicked Pharaoh in Exodus 9, “For if by now I had put forth My hand and struck you and your people with pestilence, you would then have been cut off from the earth. But, indeed, for this reason I have allowed you to remain, in order to show you My power and in order to proclaim My name through all the earth” (Ex. 9:15-16). 

 As it has been said, “God was using Pharaoh to give the world a ten-point correspondence course on who He is” (speaking of the ten plagues). With our limited human perspective and understanding, we have a hard time seeing why evil should be allowed to exist, even for a brief period of time. But, God knows and sees a lot more than we do.

The answer may have to be Deuteronomy 29:29, “The secret things belong to the Lord our God, but the things revealed belong to us and to our sons forever, that we may observe all the words of this law.”

We are simply not told, but I suspect the answer is: to see if we will fight and overcome him. Life is a test and you might say Satan makes it more intense. It’s much easier to say and do what is right in the absence of trouble and temptation.

I think the book of Job is a perfect example of this testing. Satan believed that the “blameless and upright” Job would curse God if he was put through the test of suffering, and so God stood back and allowed Satan to take away his property, his children, and his health. In Job 2:9, his wife said, “Do you still hold fast your integrity? Curse God and die!” But Job replied, “You speak as one of the foolish women speaks. Shall we indeed accept good from God and not accept adversity?” (Job 2:10). It wasn’t God directly, but He still allowed it to happen.

James 5:10-11 says, “As an example, brethren, of suffering and patience, take the prophets who spoke in the name of the Lord. We count those blessed who endured. You have heard of the endurance of Job and have seen the outcome of the Lord’s dealings, that the Lord is full of compassion and is merciful.”  Job passed the test and so the Lord blessed him greatly (read the last chapter of Job some time).

Now, even though God allows Satan to tempt man, we need to keep 1 Corinthians 10:13 in mind: “No temptation has overtaken you but such as is common to man; and God is faithful, who will not allow you to be tempted beyond what you are able, but with the temptation will provide the way of escape also, so that you will be able to endure it.”

Because when he created the first life (the Devas) they made horrible choices and he cursed the first offender into Naraka (Hell) as punishment and that Deva who is Shiva turned herself  into a man then formed an unholy union with the Demon Kali (also an offender who was cast out of the Heavens) and then Shiva who became a man and Kali created offspring that became the demonic Asura and the princes of the worlds (those are the Arch-Demon lords of each world) because Naraka and the worlds are their inheritance, and people that are righteous and don't rebel against God and who accept God's (Ishvara) love Ascend the Heavens?
  So the simple answer is because the Absolute Most Perfect God and Most Loving God created life with the option to make choices.  Maybe God wants companions instead of automated servants.

GOD has already finished what HE has ordained,SATAN is still trying to find out where to begin.

"God is working his works" does not means god works its own works..[must of been wrong first huh?] haha ..NO, sorry.. the verse means that God works his works [the lord god as the spirit of god that takes god place for us here and makes the heavens and earth his way [knowledge received] that sends us back to god last. God is not a HE."his works" means the spirit of god.. {GEN. 2:3-4 God is bless [be less] in the same day the "of' god appears next for our generations. The spirit of god takes gods place to send us back where we cannot see to begin at.

because Satan was created as an immortal being. The fact that he rebelled against God and was cast out of Heaven didn't change his nature.

it is not satan`s time to be gone yet

He lets him exist because humans chose him over the creator. He will continue to exist until humans see the results of negative choices, until he is rejected by everyone. Then hes gone. Negativity gives him life. He lives off of it

Satan has already been condemned to death, see Revelation 12:7-12; 20:10, note too what verses 13-15 says using Bibles such as the K.J.V, NWT and others as you wish. The lying allegations made against God are being answered to the extent that his name Jehovah will be sanctified or made holy and his right to rule will be vindicated for eternity, this ''court case'' has taken time and extremely soon this system under Satan's control is going to be destroyed, to learn more speak to the next JW you see or ask for a Bible study via jw.org, you can study online if you wish.

there is a free will choice of mankind. and its legalism to allow him to live, even though He did make war in heaven.
another perspective is that He allows people to choose so that in a legal way he can kick them out of the kingdom.

Satan is God's son. Man is more wicked than Satan.

god and satan are imaginary

The fact of the matter: No they are not business partners. The reason why God let Satan exist is because we became slaves to Satan and sin, because we fell from the grace of God, so God sold us to Satan and sin, as it is written Romans 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.

God and Stan are partners to rid the world of Santa and Unicorns 
while humans are collateral damage .