Does red wine vinegar need to be refrigerated?

No. Unopened vinegar will store indefinitely if kept in a cool dry place

However opened vinegar will lose its taste after about 6 months through evaporation. Refrigeration may extend that period. If vinegar becomes cloudy - sniff it to see if it smells "off" (you will be able to tell) if it seems OK you can run it through a filter paper to make it clear again.