So fungi have made the cover of Science, as parasites of bdelloid rotifers. The rotifers, which are metazoans, are asexual. So the question being addressed by these researchers is, how have these rotifers survived their pathogens for millions of years without the benefit of sexual reproduction? Sexual reproduction is considered by most biologists to be a key component of evolution, as without genetic recombination, natural selection cannot act. The answer they found is anhydrobiosis, or living without water. The rotifers are able to survive dessication, while their fungal pathogens aren't. The longer the dessication, the fewer pathogen propagules survive. The dessication also makes the rotifers lighter, which enables them to be dispersed through the air to escape.
I think there are a lot of answers to the question of asexuality within the fungi themselves. There are many, many lineages of fungi which have apparently lost the ability to undergo sexual reproduction. Like so many corners of mycology, there are several terms applied to them, Deuteromycetes (an older terms), Imperfect Fungi, or Mitosporic Fungi (cf. Meiosporic Fungi) to list three. Asexuality has developed in many fungal lineages, that is to say, the Deuteromycetes are polyphyletic. Or to say it another way, asexuality has arisen several times over evolutionary history.
