Microfabricated and self-assembled arrays of micron-sized obstacles can separate long DNA by size in several minutes due to collisions with the obstacles. In the presence of a strong field, models of such collisions normally invoke a “rope-over-pulley” approximation for the holdup time of the entangled DNA. This model suffers from a physically unrealistic singularity, where the holdup time is infinite if the two arms of the DNA rope possess equal lengths. While it is known that thermal fluctuations should lead to finite hold-up times, the latter fluctuations have not been studied in detail and are generally ignored in models of the separation process. We will present a theoretical analysis and concomitant simulation data for the idealized case of a DNA molecule that has been equally stretched on either side of an isolated, finite-sized obstacle. The theoretical model is based upon a first-passage time analysis for diffusive transport in the potential field generated by the electric field acting on either arm of the DNA. This model will be compared to probability distributions from Monte Carlo simulations of the first passage time problem, as well as Brownian Dynamics simulation data for DNA holdups in the presence of (i) a uniform electric field and (ii) the non-uniform field engendered by an insulating (e.g., PDMS) obstacle. In the latter case, transverse fluctuations of the trapped chain lead to fluctuations in the total electrical force acting on one of the arms. We will also address the relevant electric fields and time scales for this process, making a connection between the theoretical data obtained here and experimental separations.