I'm going to track back to this question more comprehensively,
but as a brief starting point lets visit the soup.
The first life-like events were likely a collection of chemical reactions that were perpetuating, there was adequate substrate, outside energy, and the products of the reaction were not toxic to additional rounds of same chemistry.
It seems to me that what makes life as we think of it is the box. The cell membrane, wall, the barrier that makes an inside and an outside. The basic feature of any inside/outside circumstance is that it allows one to make one side and the other different in some way. The key things come from this : proton/electron gradients, quite simply the ability to do work through any variety of chemistry that rely on a difference in potential. Water behind a damn, electromotive force afforded by a hydrophobic membrane separating solutes into "inside" and "outside" and using this barrier to achieve things like reducing power which affords for example carbon fixation:
http://en.wikipedia.org/wiki/Carbon_fixation
If we assume that the first life-like chemistry occurred without the benefit of cell membranes, then from a sexual/asexual sense it was an orgy. There was no barrier to complete exchange of anything and everything. Hypersexual if you will.
The cell wall/membrane changed that. Large molecules need permission to pass hydrophobic barriers. It would likely take some time to develop the means for such exchange.
So, I like to think that things started hypersexual and transited to asexual. Asexuality has consequences, impaired adaptation being among them, one simply cannot learn from and use the inventions of others.
So, the adaptive pressure to figure out sex was likely significant. Meanwhile vegetative/asexual reproduction would have to suffice. Much of this was likely afforded by "selfish genes" transposons, phage, viruses, these sorts of things out for themselves but in the course of this effecting horizontal gene flow (sex).
The long and the short is, I don't think things switch to or from sexuality or asexuality. There has always been both. the genetic blueprint for either mode of reproduction is likely in most everything.
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