Why won't off-the-shelf special cleaners eliminate washer odor for more than a few weeks?

There isn't a single washer-specific cleaner or bleach on the market that can eliminate washer odor for more than a few weeks.  Special cleaners, laundry soap, and extra bleach cycles cannot eliminate washer mold and odor because of where the mold is located.  The internal drain hose exits the pump at the bottom of the washer and winds its way toward the top of the back panel.

When you use a cleaner or bleach, it mixes only with the water at the bottom of the washer's outer drum. The washer cycle then turns the pump on and the water, mixed with cleaner or bleach, moves very quickly through the internal drain hose.  The cleaner or bleach comes in contact with the moldy hose for only a few seconds before the water along with the cleaner or bleach is out of the washer and down the drain.  When the pump turns off, the water along with the cleaner or bleach mixture inside the hose quickly drains back into the washer. Only the very bottom of the hose comes in contact with the cleaner or bleach for any period of time. Since mold in the internal hose grows from the top down, the use of specialized cleaners or bleach proves ineffective for the long term.

This is why specialized cleaners and extra bleach cycles require their use every 2-3 weeks just to keep the smell at bay.  Keep in mind that specialized cleaners and bleach mask the odor but they will not eliminate the mold or rectify the relative humidity that allowed the mold to grow in the first place.

Your clean laundry will still have a foul odor, and you can spend a small fortune buying additional cleaners.