Most homeless people are suffering from a cocktail of problems with abuse, mental illness and drugs. If you woke one one morning to find yourself on the street with ragged clothes and empty pockets in a foreign city, but you still had your wits about you, you likely wouldn't be there for long.
Most of them are in a better state then alone in a strange city, with nothing but the clothes on their back. They often have jobs, and may be living on couches or in a car, or have a bank account, or social support (Not enough to keep them in a home, but something.)
The homeless that are sleeping rough for 9 months tend to stay homeless. It is a horrible way to live, and it breaks you down really fast.
because they find a home. Think about how many people in the US are living hand-to-mouth, where any disruption can cause them to fall behind on rent. Those people make up the majority of people who have been homeless recently. They are homeless for the time it takes them to save up a deposit and find a place to live.