Why did the Lincoln administration suspend the writ of habeas corpus on occasion during the Civil War?
The reason that President Lincoln suspended the writ of habeas corpus on occasion is that he wanted to be able to hold people that he suspected of being Confederate sympathizers without having to come up with a crime to charge them with.
The writ of habeas corpus requires the government to justify the fact that they are holding someone in jail. If a writ of habeas corpus is granted by a judge, the government must tell what they intend to charge a person with.
President Lincoln did not want to have to do this. He wanted to be able to hold people indefinitely because he felt that they were a danger to the United States. He wanted to be able to do this even if, legally speaking, he would not be able to charge them with any crime.