Does radio frequency ablation kills the nerve permanently?

Yes: It kills nerves that are ablated permanently but not the nerves that are not touched.

Not usually: It usually just stuns the nerve. Dependent on the technique though - if the pain person uses higher temperatures and longer times, they can "cook" the nerve and it will not be viable any longer. Mind you there are two nerves innervating the facet joint and many anesthesia providers only treat one of them. Ask your pain doc how he/she does it.

Nothing Permanent: Usually RFA lasts at least 12-18 months on average. Some people can get less relief if nerves re-grow sooner. In my patient base most people will come back for repeat treatments at around 12-15 months. Some of my patients have had multiple years of relief. Sometimes after the 2nd or 3rd treatment the nerves grow back slower.