Pretty common ion exchange softener. My first guess might be that the resin bed is packed with some debris. Just guessing but is it possible the softener was run for a time before the filters were added? Possible changing out the resin would solve the question if it becomes a problem, but just guessing ?
When the resin picks up debris and there is no algaecide like silver used in the softener, the resin can become loaded with various types of bacteria, algae, etc. Another item which might cure it is adding a carbon impregnated with silver would clear the resin. This would likely involve pro help to get it done. The silver content makes the carbon pretty expensive and the labor to add it might make a resin tank change more practical.
But then this is also just a theory on what might be the cause.