We analyze very deep Infrared Array Camera and Multiband Imaging Photometer for Spitzer (MIPS) photometry of ~12500 members of the 14 Myr old Double Cluster, h and {chi} Persei, building upon our earlier, shallower Spitzer Cycle 1 studies. Numerous likely members show infrared (IR) excesses at 8 {mu}m and 24 {mu}m, indicative of circumstellar dust. The frequency of stars with 8 {mu}m excess is at least 2% for our entire sample, slightly lower (higher) for B/A stars (later type, lower mass stars). Optical spectroscopy also identifies gas in about 2% of systems, but with no clear trend between the presence of dust and gas. Spectral energy distribution modeling of 18 sources with detections at optical wavelengths through MIPS 24 {mu}m reveals a diverse set of disk evolutionary states, including a high fraction of transitional disks, though similar data for all disk-bearing members would provide constraints. Using Monte Carlo simulations, we combine our results with those for other young clusters to study the global evolution of dust/gas disks. For nominal cluster ages, the e-folding times ({tau}_0_) for the frequency of warm dust and gas are 2.75 Myr and 1.75 Myr, respectively. Assuming a revised set of ages for some clusters, these timescales increase to 5.75 and 3.75 Myr, respectively, implying a significantly longer typical protoplanetary disk lifetime than previously thought. In both cases, the transitional disk duration, averaged over multiple evolutionary pathways, is ~1 Myr. Finally, 24 {mu}m excess frequencies for 4-6 M_{sun}_ stars appear lower than for 1-2.5 M_{sun}_ stars in other 10-30 Myr old clusters.