The rare earth iron garnet (REIG), Eu3Fe5O12 (EuIG) has emerged as a promising material for ferrimagnetic insulator based spintronics. Earlier studies have shown that perpendicular magnetic anisotropy (PMA) in EuIG and other REIGs can be achieved by magnetostriction and misfit strain at the film-substrate interface. Typically, the strain relaxes significantly with thickness, limiting the thickness of films that can be grown using this strategy. Here we show PMA that does not reduce substantially with thickness in epitaxial EuIG films grown by off-axis sputtering; The PMA remains robust in films > 100 nm thick. Epitaxially induced strain with minimal relaxation is confirmed using high resolution symmetric and asymmetric x-ray diffraction reciprocal space maps.