In the geological past, changes in climate and tectonic activity are thought to have spurred the tempo of evolutionary change among major taxonomic groups of plants and animals. However, the extent to which these historical contingencies increased the risk of extinction of microbial plankton species remains largely unknown. Here, I analyse fossil records of marine planktonic diatoms and calcareous nannoplankton over the past 65 million years from the world oceans and show that the probability of species' extinction is not correlated with secular changes in climatic instability. Further supporting these results, analyses of genera survivorship curves based on fossil data concurred with the predictions of a birth-death model that simulates the extinction of genera through time assuming stochastically constant rates of speciation and extinction. However, my results also show that these marine microbes responded to exceptional climatic contingencies in a manner that appears to have promoted net diversification. These results highlight the ability of marine planktonic microbes to survive climatic instabilities in the geological past, and point to different mechanisms underlying the processes of speciation and extinction in these micro-organisms.