Thunderbird doesn't ordinarily impose any such limits. What is happening to lead you to say that you "cannot search for anything older than 30 days"?

Until very recently, when doing a search of either my inbox or sent box, every email (received or sent) matching the criteria I selected, would appear! Now, the search only goes back 30 or so days. It's probably something I inadvertently did myself that has caused this, but I don't know what to do to correct it!

While I was looking around for something else, I rediscovered a settings page in Thunderbird I had forgotten about.

Tools|Account Settings|{select account}|Synchronization & Storage

There are settings there for a message age limit…