It seems that BSPlayer's codec manager download an ancient version of MPA decoder (ver 1.0.0.4) released by gabest probably around 2006-2007.
Meanwhile the project was updated and there is a new release (1.6.3.5588)
Free-Codecs.com :: Download MPA Decoder 1.6.3.5588 : As the name says MPA Decoder will help to decode MPA files
Download and install, probably the bug is gone by now.
Also, as a workaround you can install CoreAAC
Free-Codecs.com :: Download CoreAAC Directshow filter 1.2.0.575 : CoreAAC is an AAC DirectShow filter decoder based on FAAD2
I am using an older version (1.0) for many years and had no problem at all.