Superconducting detectors are ideal for the search for magnetic monopoles since their sensitivity is calculated from classical properties and is independent of the particle's mass, velocity, electric charge, or magnetic dipole moment. We describe the design and the completed operation of a superconducting three-loop inductive detector to search for magnetic monopoles in cosmic rays. The three-loop detector, with a total sensing area of 476 ${\mathrm{cm}}^{2}$ averaged over $4\ensuremath{\pi}$ sr, was in operation for 1008 days. During that time, the detector logged 24 190 h of active operation. These data set an upper limit of 4.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{s}}^{\ensuremath{-}1}$ ${\mathrm{sr}}^{\ensuremath{-}1}$ at 90% C.L. ($\frac{2.3}{\ensuremath{\int}dAd\ensuremath{\Omega}\mathrm{dt}}$) on any uniform flux of magnetically charged particles of any mass passing through the Earth's surface at any velocity.