The reported positions of 964 suspected nova eruptions in M31 recorded through the end of calendar year 2013 have been compared in order to identify recurrent nova (RN) candidates. To pass the initial screen and qualify as a RN candidate, two or more eruptions were required to be coincident within 0.‧1, although this criterion was relaxed to 0.‧15 for novae discovered on early photographic patrols. A total of 118 eruptions from 51 potential RN systems satisfied the screening criterion. To determine what fraction of these novae are indeed recurrent, the original plates and published images of the relevant eruptions have been carefully compared. This procedure has resulted in the elimination of 27 of the 51 progenitor candidates (61 eruptions) from further consideration as RNe, with another 8 systems (17 eruptions) deemed unlikely to be recurrent. Of the remaining 16 systems, 12 candidates (32 eruptions) were judged to be RNe, with an additional 4 systems (8 eruptions) being possibly recurrent. It is estimated that ∼4% of the nova eruptions seen in M31 over the past century are associated with RNe. A Monte Carlo analysis shows that the discovery efficiency for RNe may be as low as 10% that for novae in general, suggesting that as many as one in three nova eruptions observed in M31 arise from progenitor systems having recurrence times ≲ 100 yr. For plausible system parameters, it appears unlikely that RNe can provide a significant channel for the production of Type Ia supernovae.