The very-high-energy (VHE) gamma-ray spectrum of the extreme blazar 1ES 0229+200 as observed by imaging atmospheric Cherenkov telescopes (IACTs) is surprisingly hard and only weakly variable. Several theories advanced to explain the VHE observations of this source invoke the interactions of cosmic rays along the line of sight, leading to predictions of observable gamma-ray emission that is steady on year-long time scales, with energies well in excess of the cutoff expected from attenuation by the extragalactic background light. The High Altitude Water Cherenkov (HAWC) observatory is ideally suited to investigate this scenario due to its excellent sensitivity at multi-TeV energies, its continuous monitoring of the source over several years, and the declination of the source which maximizes the HAWC sensitivity. Over the past three years, HAWC has collected the world's most sensitive data set on 1ES 0229+200 at multi-TeV energies, allowing us to place strong constraints on the VHE emission from line-of-sight interactions from this source. In this presentation, we discuss the implications of the non-observation of 1ES 0229+200 in the HAWC data set in terms of the long-term gamma-ray emission from this source, focusing especially on models involving line-of-sight interactions of cosmic rays.