A resilient system design problem is formulated as the quantification of uncommitted reconfigurable resources required for a system of components to survive its lifetime within mission availability specifications. We show that this survivability metric can be calculated according to the residual functionality obtained from pools of dynamically configurable elements constituting the amorphous resource pool (ARP). The ARP is depleted based on the failure rate to replenish the functionality lost in a reconfigurable fabric due to the occurrence of permanent faults during the mission lifetime. While genetic algorithms are selected for the reparation method, any probabilistic or deterministic active repair strategy is covered without loss of generality. Parameters of this model are correlated with reliability specifications of Xilinx Virtex-4 field programmable gate array devices, which are then utilized for MCNC benchmark circuits along with a realistic space mission. Calculation of the spare fabric resources which must be budgeted for a mission, maximum mission lifetime, and repair policy parameters are realized using the proposed probabilistic survivability model for soft computing-based repair strategies.