A customer has informed us that they are going to another vendor - how to say sorry to see you go and let them know if they need us in the future we are here for you

You just said it. Short and simple without any drama.

"Sorry to see you go. If you need us in the future, we are here for you."

As the others have said, short , sweet and honest is the best way... otherwise it will make them feel like you are trying a hard sell on them... and it will backfire.

Depending on your product or service, I might invite one of them to lunch to discuss the reasons, and be prepared to offer lower prices, faster delivery, etc. if you can.