Heterodea is now a synonym of Cladia. This might be Cladia muelleri. Though you say they are out with the rain and gone after a few days of sun - the latter is not in fact the case. In dry conditions this lichen curls up, shrivels a bit and becomes dormant, so all you see is the dark underside, which is very easy to overlook in the leaf/twig litter in which this species is often found. After some rain, the lichen uncurls, the upper surface (dull when dry) becomes a brighter green, very easily visible and the algal partner then gets back to photosynthesizing. It is quite astounding how well, what is say the size of an outstretched hand when moist, can hide when dry. When dry the lichen is very brittle, but it is pliable when moist.