In at least some asexually reproducing oligochaetes, this genetic rigidness is overcome by alternating between sexual and asexual forms. Generally, the worms stay asexual, reproducing for example by architomy, during favourable or stable conditions, and therefore quickly spread. When conditions deteriorate, or the environment becomes unstable, they switch to sexual reproduction, and then - often - die.
This cycle can be as short as a year in some species, with asexual reproduction throughout summer and autumn, and sexual reproduction kicking in when it gets colder. In some (all?) cases, the worms die after having reproduced sexually and deposited their offspring in cocoons.
See, for example, L. C. Armendáriz, Hydrobiologia 438: 217-226, 2000.
Further some fishes (and I believe there are some very large ones outside Madagascar who belong in this group) reproduce asexually but sperm-dependantly through gynogenesis. Sperm from a closely related species is needed to stimulate embryogenesis, but does not contribute genetically to the offspring. Naturally, all individuals of these fishes are female.
Other fishes display hybridogenesis, but even though I understand all the words in its descriptiuon, I am not entirely sure how it works.
See, for example, M. J. Alves, M. M. Coelho, and M. J. Collares-Pereira, Genetica 111: 375-385, 2001. This paper contains a description of hybridogenesis which I do not fully understand. It's there, though.