I work for a church doing web design and we are currently using WordPress with a premium theme we purchased from a third-party company.

We customized the theme for our church and everything looked great until we started experiencing some recent problems.

The theme company said they updated the theme to fix the changes, but when I did the customizations I edited the theme itself instead of making it a child theme (I was pretty new to web design).

If I update the theme now, it will undo all of our changes. Is there any way to update the website theme while keeping the customizations without the website having to be down for a long time?

I want this to be a permanent fix so that the theme can automatically be updated in the future without any problems.

What kind of changes did you make? Was it all CSS?

It was mostly CSS, but with some changes to a few php files.

You will definitely need to create a child theme then.

Here's a guide on how to do that. http://codex.wordpress.org/Child_Themes
If you're unsure how to start, ask the developers to get you started with the right files.