The premise of classical hydraulic fracture breakdown models is that hydraulic fracture growth can only commence when the wellbore pressure reaches a critical value, sufficient to overcome the tensile strength of the rock. However, rocks are well-known to exhibit static fatigue, that is, delayed failure at stresses below the tensile strength. In this paper we explore the consequences of delayed failure on initiation of multiple hydraulic fractures. Specifically, given a certain breakdown pressure, we investigate the conditions under which subsequent hydraulic fracture(s) can initiate within the timeframe of a stimulation treatment in regions of higher stress and/or strength due to delayed failure mechanisms. The results show that wells completed in shallower formations are more sensitive to variations in strength while wells completed in deeper formations are more sensitive to variations in stress. Furthermore, cases in which all hydraulic fractures breakdown according to the same pressurization regime, that is, all are "fast" (non-fluid-penetrating) pressurization or else all are "slow" (fluid-penetrating) pressurization cases, are highly sensitive to small stress/strength variability. On the other hand, if the first hydraulic fracture initiation is in the "fast" pressurization regime and subsequent fracture(s) are in the "slow" pressurization regime, then the system is robust to a much higher degree of variability in stress/strength. Practically, this work implies that methods aimed at moderately reducing the variability in stress/strength among the possible initiation points (i.e. perforation clusters) within a particular stage can have a strong impact on whether multiple hydraulic fractures will initiate. Additionally, this analysis implies that pumping strategies that encourage "fast", non-penetrative breakdown of the first initiation point followed by the opportunity for fluid-penetrating, "slow" breakdown of subsequent initiation points could be highly effective at encouraging multiple hydraulic fracture initiation.