Luminous debris disks of warm dust in the terrestrial planet zones around solar-like stars are recently found to vary, indicative of ongoing large-scale collisions of rocky objects. We use Spitzer 3.6 and 4.5 {μ}m time-series observations in 2012 and 2013 (extended to 2014 in one case) to monitor 5 more debris disks with unusually high fractional luminosities ("extreme debris disk"), including P1121 in the open cluster M47 (80 Myr), HD 15407A in the AB Dor moving group (80 Myr), HD 23514 in the Pleiades (120 Myr), HD 145263 in the Upper Sco Association (10 Myr), and the field star BD+20 307 (>1 Gyr). Together with the published results for ID8 in NGC 2547 (35 Myr), this makes the first systematic time-domain investigation of planetary impacts outside the solar system. Significant variations with timescales shorter than a year are detected in five out of the six extreme debris disks we have monitored. However, different systems show diverse sets of characteristics in the time domain, including long-term decay or growth, disk temperature variations, and possible periodicity. ; Comment: 50 pages, 14 figures, 9 tables; Accepted for publication in the Astrophysical Journal