Actually, there are a number of critters, even today, that sometimes reproduce sexually and sometimes asexually. The most commonly known is the paramecium, a one-celled animal that reproduces normally by fission. Sometimes, however, under crowded conditions, two paramecia get together and exchange genetic material to reproduce.
You can read all about it here:
http://ebiomedia.com/gall/classics/Paramecium/paramecium4.html
Actually the common yeast falls into this category also. There are very few microbes that don't have some sort of sexual cycle and acquiring it or losing it happens all the time.