My ex won't refinance to take my name off the mortgage
Your lender was not part of your divorce and is not bound by your decree. A judge can order your ex to refinance, but no judge can make a bank approve them. Until someone qualifies for a new loan, your name stays on the old one.
That single fact explains why this situation is so common and why calling the lender does not fix it.
What it is costing you meanwhile
This is not a paperwork annoyance. While your name is on the mortgage:
Their late payment is your late payment. It lands on your credit report identically, no matter who lives in the house or what the decree says.
The monthly payment counts against you, unless you get it excluded. Lenders count the mortgage payment, not the balance, in your debt-to-income ratio. And there is a way out that people rarely ask for: Fannie Mae, Freddie Mac, and FHA all let a lender exclude a mortgage payment that a divorce decree assigned to your ex. Fannie's rule needs only the decree, and so does FHA's: FHA normally asks for 12 months of payments by the other party, but says in so many words that this is not required when a court order created the obligation, and asks only for a copy of the decree. So nobody should tell you to wait a year. Bring the decree to the loan officer and ask for the court-ordered-assignment exclusion by name, because it can be the difference between qualifying and not. It only clears the payment going forward, though. Any late payments on that loan from before the decree assigned it still sit in your file, which is one more reason to keep a joint mortgage current until the decree lands.
You carry the risk without the asset. If the loan defaults, your credit takes the damage, and if you also signed the house over, you have no ownership left to show for it.
Why they may not be refusing
Worth separating, because the response differs. Sometimes an ex is stalling. Often they genuinely cannot qualify: their income alone does not support the loan, rates have risen since you bought, or the house is worth less than the balance. A person who cannot refinance is not made able to by a court order.
You may be able to find out. Ask, in writing, whether they have applied and what the lender said. A refusal to answer is itself informative, and the written record matters later.
What actually gets this fixed
Read your decree first. Look for a refinance deadline and a remedy: language saying what happens if it does not occur by a date, usually that the house goes on the market. If your decree has that, you have a path: the deadline passed, the condition triggered, and you ask the court to enforce it.
If your decree has a deadline, enforce it. That is a motion asking the court to make your ex do what was already ordered. Courts have real tools here, including ordering a sale, and in some circumstances awarding you the fees you spent bringing the motion.
If your decree is silent, you have a harder problem. Property terms generally cannot be modified the way support and custody can, so the realistic route is asking the court to clarify what it already ordered rather than to rewrite it. This is the most common expensive gap in a decree, and it is worth reading which decree provisions are actually enforceable if you are still at the drafting stage.
A sale ends it cleanly. Nobody enjoys this answer, but selling is the only route that reliably removes your name without depending on your ex qualifying for anything.
What does not work
Assuming a refusal and never asking. Ask in writing for a release of liability, which is the industry term. On a VA loan you may not even need an assumption: the decree plus a recorded quitclaim can be enough. On an FHA loan there is a form for it, and in a divorce FHA can allow the assumption without running credit on your ex at all, but only on its own terms: the spouse staying on the title has to be living in the house, and has to have been making the mortgage payments for at least six months before applying. Someone who moved out does not fit it. The real obstacle is usually that your ex has to qualify on their own, not that the servicer has no process, and servicers refuse these wrongly often enough that the CFPB has published a report on it. If you are refused, you can complain to the CFPB.
Waiting quietly. Every month of waiting is another month of exposure, and delay tends to make the numbers worse rather than better.
Signing a quitclaim deed to "get it over with." That gives up your ownership while leaving the debt exactly where it was, which is the worst combination available. The difference between the deed and the mortgage is the thing to understand before signing anything.
What a court can order, how enforcement works, and whether fees can be shifted to the non-complying party all vary by state. If a refinance deadline in your decree has passed, that is worth a conversation with a licensed family-law attorney sooner rather than later, because delay tends to narrow the options.