Azaleas and rhododendron shrubs, both members of genus Rhododendron, should only be fertilized sparingly in late autumn or early spring, if at all. The American Rhododendron Society suggests that these shrubs should only be fertilized if they obviously display some sort of deficiency.
Both the Society and the Old Farmer's Almanac warn that heavy or periodic fertilizer application can burn the plant, causing extensive root damage and possibly killing the plant. Mulching rhododendron species with sawdust and wood chips tends to leach nitrogen away from the shrubs. Adding a fertilizer like ammonium sulfate can resolve this issue, though it is generally easier to simply avoid these types of mulch. Phosphorous, magnesium, calcium and iron deficiencies in the shrubs are also a concern depending on the type of soil in which they are growing.