We characterize the sensitivity of imaging properties of a layered silver-TiO₂ flat lens to fabrication inaccuracies. The lens is designed for approximately diffraction-free imaging with subwavelength resolution at distances in the order of a wavelength. Its operation may be attributed to self-collimation with a secondary role of Fabry-Perot resonant transmission, even though the first order effective medium description of the structure is inaccurate. Super-resolution is maintained for a broad range of overall thicknesses and the total thickness of the multilayer is limited by absorption. The tolerance analysis indicates that the resolution and transmission efficiency are highly sensitive to small changes of layer thicknesses.