What a fascinating word "wit" is! As a noun, it comes in both a discrete and continuous varieties. (English teachers like to use the words "countable" and "uncountable", but I avoid those words because I have trouble keeping them straight.) You can have "much wit" or you can have "a wit". Shakespeare believed there to be five wits, or specialized forms of intelligence: common wit, estimation, memory, imagination, and fantasy. Those five "wits" give us a good idea what "wit" means. It is intelligence, but not just any intelligence. It is *sharp*, *precise* intelligence. What a shame it would be if you lost all of them! Don't lose your wits! Sense of humor is a special kind of intelligence. It is a type of sharpness. That's why funny people are "witty". On the other hand, being without wits (or without "wit" - you really can't go wrong - don't worry about whether "wit" is countable or not - the word likes to challenge your wits, or wit, or whatever) leaves you "witless", which is a synonym for the modern terms "clueless" or "foolish".

To keep your wits / To not lose your wits means to keep (or not lose) your ability to think clearly and make decisions. Your wits are your ability to think clearly.

More context might be helpful, but it sounds like they were saying something like she didn't lose her mental health, she didn't go insane, she didn't become senile, she didn't lose touch with reality, etc.