Sounds like you’ll need to leverage Invoice History. 

If data was removed during Period End / Year End processing, there is likely no way to bring it back.  If you have an archive (company copy) you could refer to the older data there, but there is no way to merge purged data back into your Live company code.  (Don't even try...).

What I have done is to make copies of the company at year end. There have been incidents where I went back to companies I saved 4-5 years ago to look at data that was no longer present in the live company.

Luckily, I make copies of the company pretty often. But just to confirm: once the number  of years has been reached, the history just goes away? 

Yes, it just goes away, during Period End / Year End processing.

What if PE/YE processing hasn't been done?