To avoid over-designing wave energy converters (WECs), their reliability and survivability aspects need to be accurately addressed. The most common failure modes are: instantaneous failure due to high instantaneous loads, and fatigue failure due to the accumulated damage in the structure during years of operation. Here, we present a fatigue analysis of a point-absorber WEC in sea states corresponding to a 50-year environmental contour from the Dowsing site, UK. The data for this analysis is generated by a WEC-Sim model that is calibrated with a 1:30 scaled WEC from a wave tank experiment. In this study, the partial damage in each 1-hour sea state sample is calculated using the rainflow counting and Palmgren-Miner rule. Then, considering the joint probability density function of the sea states, the equivalent two-million cycle load is 2.42 MN for the full-scale system considering the accumulated damage in 50 years of operation. In a comparison of the fatigue limit state (FLS) and ultimate limit state (ULS), it was found that the ULS is the governing limit state in the design of the WEC system here.