Asexual species accumulate deleterious mutations through an irreversible process known as Muller's ratchet. Attempts to quantify the rate of the ratchet have ignored the role of temporal environmental heterogeneity even though it is common in nature and has the potential to affect overall ratchet rate. Here we examine Muller's ratchet in the context of conditional neutrality (i.e., mutations that are deleterious in some environmental conditions but neutral in others) as well as more subtle changes in the strength (but not sign) of selection. We find that temporal variation increases the rate of the ratchet (mutation accumulation) and the rate of fitness decline over that of populations experiencing constant selection of equivalent average strength. Temporal autocorrelation magnifies the effects of temporal heterogeneity and can allow the ratchet to operate at large population sizes in which it would be halted under constant selection. Classic studies of Muller's ratchet show that the rate of fitness decline is maximized when selection is of a low but intermediate strength. This relationship changes quantitatively with all forms of temporal heterogeneity studied and changes qualitatively when there is temporal autocorrelation in selection. In particular, the rate of fitness decline can increase indefinitely with the strength of selection with some forms of temporal heterogeneity. Our finding that temporal autocorrelation in selection dramatically increases ratchet rate and rate of fitness decline may help to explain the paucity of asexual taxa.