The species is thought to have survived the arrival of the first settlers in the Canary Islands, and become extinct after the arrival of European settlers in the 15th century. It is suspected that the species became extinct due to hunting pressures and possibly the arrival of introduced species such as rats.
References
J. C. Rando, J. A. Alcover (2008) "Evidence for a second western Palaearctic seabird extinction during the last Millennium: the Lava Shearwater Puffinus olsoni" Ibis150 (1), 188–192 doi:10.1111/j.1474-919X.2007.00741.x