We have an end date for BCC’s Season 4, as well as some additional information about Arena points and their post-season conversion, and the pre-patch costs of S4 gear. 

Season 3 (Source)

On the eve of the Wrath Classic pre-expansion patch, we will end the final season of Burning Crusade Classic PvP at 10:00 p.m. in each region. In this region, Season 4 will end at 10:00 p.m. PDT on August 29.

During maintenance on August 30, we will update the game, and all Arena points will be converted to Honor. Throughout the pre-patch, Arena Season 4 gear will be sold for Honor.

Good luck fighting to the finish!