I was thinking about lights in elementary school recently when I remembered how often after a power failure, there would be a some troffers in the hallways that wouldn't come back on. I'm pretty sure it was a ballast issue since it was usually whole troffers. So can power cycles on 24/7 fixtures adversely affect them?

This is one of those cases where those ballasts rack up 1000's of hours (possibly even exceeding their rated lifespan). Everything is good & stable, but then a power outage happens...its not so much the outage itself, but the fact it allows things to fully cool down. Components within the ballast that are in marginal condition(simply from all those hours) are fine when they're already warm & operating, but once they've cooled off, they may change properties *just enough* that that coupled with startup(the most stressful time on any electronics) is when a failure happens.