When you have a customer that you’ve completed the work for and they’re ready to move on, there’s NO REASON to force them to stay. If they’ve completed their contractual obligation and they want to move their website to another host, Let. Them. Go.
By forcing someone to stay with you after they’re ready to move on, the only thing you’re doing is hurting your company for a little extra money from the client. What you won’t get is a good endorsement down the road. You won’t get a good review. You won’t get a referral. You WILL get a bad review. You will get someone who will trash your name any chance the topic of their website or marketing comes up.
An unhappy customer will be your worst nightmare. They will make your life miserable. So, why take their website hostage when they’re ready to move on? Why not help them get it setup on their new host? Why not help them? They’ve paid you your money. Let them go.