It does sound unfair, but see here for supporting sources https://www.nolo.com/legal-encyclopedia/tenants-right-break-...
Going into court you have no/low knowledge of what your landlord has actually done. If they pull out their ads they posted on the internet or on some zero readership newspaper. The judge will see they have made an effort and you probably are grasping at straws because you have nothing in the way of proof. If you’re lucky, judge would hear some expert testimony (realtor) that says the apartment/market/etc should have been filled within 1-2 months and they feel it’s highly unusual the unit would remain unfilled for 6 months. But even still, if the law says the landlord is required to market the property it might not imply they have to be good at marketing the property. So there’s a grey area where it could go either way, and he can proof that you can’t match.