Can I get my leave for Christmas approved during an investigation?

Your commander is the approval for leave, they denied it.

Imagine your question in this manner:
You're a child and you ask your parents if you can play video games. They say no. Then you go on the internet and ask, "My parents said I can't play video games, who can I ask that will let me play video games?"
That's the equivalent of your question, the person who says yes already said no.

Ask your attorney. Otherwise, get one and stay off public forum.

You're being serious with this question?

NO<NO<NO- see SFC Boyd's comment. You are temporarily flagged until the investigation is concluded, or CID says you are no longer of interest. It doesn't matter if it takes months.

My guess is if it is you being investigated they cancelled it because you are a AWOL risk in their eyes. You only chance is to go see your commanding officer through request mast if he won't see you any other way. If I were in your shoes I would put in the request mast to the highest level in your command to save time from having to resubmit in the event your leave is denied. Good Luck

Somehow you are involved in a situation where your presence is required to complete the investigation. If you are the one being investigated, leave may be the least of your problems. If you are just a witness, either pick your friends more cautiously or realize you are necessary to determine someone else's future or to determine whether a procedure must be modified..

This is an issue you need to address with your current chain of Command. They are the only ones who can change this.