If you are in an accident where other driver is at fault and their insurance is covering car rental what can you do if insurance stops paying for car rental but car is still in shop being repaired?

Ask the insurance company why they are no longer paying the rental bill. If they have accepted liability the only reason they would stop paying would be due to the repair shop taking excessive time to complete the repairs. (In the insurance company's opinion). Although you will be roped into this, it should be between the insurance company and the body shop. If the insurance company won't budge ask the repair shop to pick up the remainder of the rental bill until repairs are complete. This is common in this industry.