This is not just an issue with replacement batteries from iFixit for the 2011-12 MacBook Air 13 inch running El Capitan. I am having this exact problem with batteries from OEMs: SMP and Newer Tech. It will not charge with the OEM battery.
Took the machine to the Apple Genius Bar, and everything is perfect -- just the battery is shot. Seems like Apple need to re-write some code in El Capitan 10.11.7 to fix the issue.