The basic problem of collisional end loss of electrostatically confined particles in a magnetic mirror field with a multi-species background plasma is considered. An analytical procedure similar to, but more accurate than, that of Pastukhov is employed. Using the method of images, in the limit of large mirror ratio and modest confining potential, a class of approximate solutions, {Fa}, to the corresponding linearized Fokker-Planck equation is found, which is characterized by some adjustable parameters. These parameters are then chosen so that the surface of Fa = 0 approximately matches the true loss boundary. An analytical estimate of the error in the loss rate due to this matching procedure is made. A new expression for the loss rate is developed and compared with the results from Fokker-Planck codes, and remarkable agreement over a wide range of mirror ratios and confining potentials is found.