You can have it stay up there as long as your story needs it to stay up there.

People sometimes climb up into trees and kill themselves. I remember reading about one such that winter hikers spotted. The body had been up there for years. I could not find that one again but here are others.

1. https://www.dailymail.co.uk/news/article-2100499/Melissa-Joy-Dietzel-Decomposing-body-woman-30ft-tree-Sydney-missing-US-tourist.html

Her body was up in the tree for 2 weeks. It was a populated area and people smelled it.

2: https://www.bournemouthecho.co.uk/news/11404359.suicide-verdict-for-missing-21-year-old-found-in-tree-at-meyrick-park-golf-club/

This body was in the tree for three years. In a park!

3: https://www.telegraph.co.uk/news/worldnews/europe/germany/5098610/Skeleton-found-in-tree-29-years-after-suicide.html

This body was a skeleton, found after 29 years.

Summary - if you want it to fall out after 3 days, fine. But decomposition is a lot slower up off the ground. Ants, worms and things like that access the body from the ground and a body on the ground will also stay moist which facilitates decomposition. Dogs, armadillos and the like will not be able to get a body in a tree and depending how deep it is, vultures might not either.

That leaves insects. In your scenario, I suspect fly maggots will eliminate the soft parts while it is summer; that will also eliminate much of the ability of the corpse to hang on to moisture. Once the weather cools the insects die off and then what is left will desiccate in the dry cool winter. The desiccated sinews and muscles will hold the skeleton together and are not very attractive to scavengers. If you need it to stay up there lodged in the branches for decades, that can happen.

You can have it stay up there as long as your story needs it to stay up there.

People sometimes climb up into trees and kill themselves. I remember reading about one such that winter hikers spotted. The body had been up there for years. I could not find that one again but here are others.

1. https://www.dailymail.co.uk/news/article-2100499/Melissa-Joy-Dietzel-Decomposing-body-woman-30ft-tree-Sydney-missing-US-tourist.html

Her body was up in the tree for 2 weeks. It was a populated area and people smelled it.

2: https://www.bournemouthecho.co.uk/news/11404359.suicide-verdict-for-missing-21-year-old-found-in-tree-at-meyrick-park-golf-club/

This body was in the tree for three years. In a park!

3: https://www.telegraph.co.uk/news/worldnews/europe/germany/5098610/Skeleton-found-in-tree-29-years-after-suicide.html

This body was a skeleton, found after 29 years.

Summary - if you want it to fall out after 3 days, fine. But decomposition is a lot slower up off the ground. Ants, worms and beetles access the body from the ground and a body on the ground will also stay moist which facilitates decomposition. Coyotes, armadillos and the like will not be able to get a body in a tree and depending how deep in the branches it is, vultures might not either. It is those big animals that pull a corpse apart.

What is left is insects and they will leave the skeleton intact. In your scenario, I suspect fly maggots will eliminate the soft parts while it is summer; that will also eliminate much of the ability of the corpse to hang on to moisture. Once the weather cools the insects die off and then what is left will desiccate in the dry cool winter. The desiccated sinews and muscles will hold the skeleton together and are not very attractive to scavengers. If you need it to stay up there lodged in the branches for decades, that can happen.