Is the pickup an exact equal distance from every string, or at least an exact equal distance from the two outside strings? It's possibly just one of these issues:
saddle too high. If intonation is proper for all the other strings, but sharp for the A, this would be the easiest diagnosis.
pickup slanted (apparent loudness of some frequencies is less than others, in spite of equal distance). check the mm's between all strings. the outside ones should be near identical distance afaik
I don't know enough about guitars and electronics otherwise. it could even be a mid-freq cut happening internally or at amp. Could you provide more info?
Amp and watt value.
where any knobs are set for treble/mid/bass.
pickup height and level, string height in relation. The strings are supposed to make a slight arc afaik