"Non-blooming daylilies" is what your English teacher called an "oxymoron"–a term that combines contradictory meanings. Not many problems plague these sturdy perennials but there may be one or more reasons that they don’t bloom with their customary vigor.
New daylilies often need a few years of growth to bloom. If yours are new divisions or grown from seed, they may simply need to mature.
Crowns should be planted about 1 inch below the surface. Plants set too deeply may eventually pull themselves upward but don’t bloom well in the meantime.
Bloom fails as clumps grow too dense with age or when plants are set too closely. Divide old clumps and set new plants 1 to 3 feet apart.
Although a few varieties bloom in full shade and some fade in full sun, most daylilies depend on at least a few hours of morning sunlight–or dappled sunlight–to bloom properly.
Garden fertilizer confuses daylilies; its use encourages vegetative growth at the expense of bloom. Some gardeners use a bit of garden fertilizer in fall after spring planting to aid root development and a fast vegetative start the following spring. All that adult daylilies need to thrive is a helping of compost in summer and fall mulches.