This sounds as though it could well be the narcissus eelworm - Ditylenchus dipsaci - an infestation of which causes layers in the bulb to go brown. If you cut the bulb horizontally there will be a brown ring on the cut surface, and if you cut it vertically you will see a brown layer following the vertical profile of the bulb. If the infestation is severe there are often yellowish swellings on the leaves.
The normal (and simplest) treatment is simply to dig up all the infected bulbs and any others nearby and burn them - the nematode spreads through the soil. However, narcissus eelworm, like chrysanthemum eelworm, can be eradicated by heat sterilisation if you have the equipment and patience. In the case of narcissi this consists of immersing the bulbs in water at a temperature of 45 deg. Centigrade for 3 hours. For the treatment to be effective the water temperature should not drop during the treatment - any lower temperature will not kill the pests - and a few deg. higher will kill the bulb. Unfortunately, although this operation kills the eelworm, the affected layer will often rot anyway and the bulb still dies.
Whatever method you adopt, narcissi should not be planted in the same spot for a minimum of 2 years