How do I keep my butter based syrup or sauce from separating?

Sometimes my butter based syrup separates once it’s cooling, or after it’s reheated a couple of times. Then, when I try to reincorporate it by stirring, the consistency is never the same and the taste is off too.
How do I prevent my syrup from separating?
I’m thinking that the times it separates after it’s initially cooked, and it’s cooling, is because it didn’t cook long enough and/or wasn’t stirred enough as it cooked maybe?
But if it’s perfect and after it cools there’s no separation..why does it separate after it’s reheated. Is there a way to prevent this?

Advice appreciated.