  We investigate the effect of the hot CNO cycle breakout reaction
15O(alpha,gamma)19Ne on the occurrence of type I X-ray bursts on accreting
neutron stars. For f_rp <~ 0.1, where f_rp is a dimensionless factor by which
we multiply the 15O(alpha,gamma)19Ne reaction rate of Caughlan & Fowler (1988),
our model predicts that bursts should occur only for accretion rates below a
critical value of approximately 0.3 times the Eddington limit. This agrees with
observations. For larger values of f_rp, including the standard choice f_rp =
1, the model switches to a new regime in which bursts occur all the way up to
roughly the Eddington limit. Since the latter regime disagrees with
observations, we suggest that the true 15O(alpha,gamma)19Ne reaction rate is
lower than usually assumed.
