In the hose? (Some inflator designs, such as Aqualung and Cressi, include another Schrader valve.)This happened to me as well. Replace the Schrader valve. It’s cheap, easy and it solved my issue.
I am having trouble understanding how a hose schrader valve problem could lead to a BCD inflation, since the valve is opened by and held open by the QD nipple on the inflator. It does NOT open and close during the operation of the inflator, that is a different mechanism.