The loss-cone-driven electron cyclotron maser instability is widely believed to be responsible for millisecond bursts of intense microwave emission often observed during solar flares. However, the maser radiation is strongly absorbed as it propagates outward from the corona and existing analytical models predict that this absorption should be sufficiently strong to prevent observable levels of the radiation from escaping, except under highly restrictive conditions. In order to address the problem of how microwave spike bursts can be observed at all, we present a numerical ray-tracing analysis which incorporates emission, propagation and absorption of fundamental cyclotron maser radiation in a realistic model of a coronal flux loop. It is found that the radiation can escape to a potential observer and that the physical conditions under which escape occurs are more restrictive for fundamental emission in the extraordinary (x)-mode than in the ordinary (0)-mode. Escaping radiation in the x-mode is found to be highly directional and chiefly observable toward the center of the solar disk, while escaping 0-mode radiation is found to emerge from the corona over a much wider range of directions, with some cases corresponding to observable radiation near the solar limb.