To be excessively unreliable, and flake out. To frequently "Asian-Out" is to bail on almost every event/meeting/thing you agree to attend. The excuses provided will commonly be along the lines of, "My mother cooked me dinner and is waiting for me at home," or "I just found out I have to go to a family member's wedding, sorry".
"I really hope Priya doesn't asian-out on us again tonight."
"Sadaf you are not allowed to asian-out on me!"