The only way you'd call the term 'aerodrome' dead is the form where it was the name of an actual flying machine, eg Langley's Aerodrome. It has to be said we don't walk out in the morning saying "I'll just take the old aerodrome up for a spin."
However, if we're talking places where flying machines operate from, then aerodrome is alive and well.
Collins Dictionary, you can get stuffed.