Long‐term data characterizing the oceans' biological carbon pump are essential for understanding impacts of climate variability on marine ecosystems. The “Bakun upwelling intensification hypothesis” suggests intensified coastal upwelling due to a greater land‐sea temperature gradient influenced by global warming. We present long time series of bathypelagic (approximately 1,200–3,600 m) particle fluxes from a coastal (CBeu: 2003–2016) and an offshore (CBmeso: 1988–2016) sediment trap setting located in the Canary Current upwelling. Organic carbon (Corg) and biogenic opal (BSi, diatoms) fluxes were twofold to threefold higher at the coastal upwelling site compared to the offshore site, respectively, and showed higher seasonality with flux maxima in spring. A relationship between winter and spring BSi fluxes to the North Atlantic Oscillation index was best expressed at the offshore site CBmeso. Lithogenic (dust) fluxes regularly peaked in winter when frequent low‐altitude dust storms and deposition occurred, decreasing offshore by about threefold. We obtained a high temporal match of short‐term peaks of BSi and dust fluxes in winter to spring at the inner site CBeu. We found synchronous flux variations at both sites and an anomalous year 2005, characterized by high BSi and Corg fluxes under a low North Atlantic Oscillation. Corg and BSi fluxes revealed a decreasing trend from 2006 to 2016 at the coastal site CBeu, pointing to coastal upwelling relaxation during the last two decades. The permanent offshore upwelling zone of the deflected Canary Current represented by the flux record of CBmeso showed no signs of increasing upwelling as well which contradicts the Bakun hypothesis.