I've just noticed some dead leaves on the two Rhododendrons and one of the branches seems to be lifeless. From early in the spring I apply Osomote around the base of the shrub and then in mid-summer as well. Any and all advice would be greatly appreciated.

Drought can cause some leaves, entire branches or entire plants to die. Make sure that the soil is getting sufficient moisture through the black plastic (the soil should feel moist, not dry or wet). Too much wetness at a depth of 4" or so can cause root rot. Research if borers may have also damaged the affected branch(es).

Appreciate your advice. We have all experienced one hot hot summer. I check on the root as you suggested.