The convergence of eXtremely Large (XL) antenna arrays and high-frequency bands in future wireless networks will inevitably give rise to near-field communications, localization, and sensing. Dynamic Metasurface Antennas (DMAs) have emerged as a key enabler of the XL Multiple-Input Multiple-Output (MIMO) paradigm, leveraging reconfigurable metamaterials to support large antenna arrays. However, DMAs are inherently lossy due to propagation losses in the microstrip lines and radiative losses from the metamaterial elements, which reduce their gain and alter their beamforming characteristics compared to a lossless aperture. In this paper, we address the gap in understanding how DMA losses affect near-field beamforming performance, by deriving novel analytical expressions for the beamforming gain of DMAs under misalignments between the focusing position and the intended user's position in 3D space. Additionally, we derive beam depth limits for varying attenuation conditions, from lossless to extreme attenuation, offering insights into the impact of losses on DMA near-field performance.