Hello Oliver, you should always be up to date with the latest version of WordPress. It creates a security vulnerability if you are not, and of course, it can cause things to break. It would be like never changing the oil in your car.
First you can create a backup just in case, so you can revert to an old version of your site if something does happen during update. Then work out the issues of the update in another place, and when they are worked out, you can then make the fully updated site live.
I would also recommend subscribing to VaultPress, which would be an easy one-click restore for you.
We can only support the latest versions of all our plugins and add-ons, running on the latest version of WordPress and on the Twenty Eleven theme.
I hope this helps!
Joyce