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.

Ah that makes sense!

What is the standard ballast lifespan? They're never printed on the ballasts themselves

The standard life rating is hidden behind the reliability ratings (like MTBF,...), but that is often published only in the corresponding technical documentation (datasheets,...), not on the product label/etch itself, nor on the distribution package box. The rating is supposed to indicate how many failures you should anticipate per some time when operating your larger installation, it does not differentiate if these are really normal wear or random defects.

Usually the corresponding lifetime uses to be in the 100kHour ballpark...

battery back-up fixtures will fail quicker and will also cause the lamps they power to fail quicker as well.  I've changed out quite a few battery packs and those isolated ballasts for T8 fixtures over the past 20 or so years.  Ironically, we didn't see this type of behavior as much on the T12 emergency battery packs and ballasts. 

Batteries in the emergency fixtures are consumable material, they are supposed to be replaced within 4 years for most types, the "100khour" is for the part that "suppose to last long", like the ballasts, connectors, but also fixture body, reflectors, covers (cracked or unsightly discolored cover is also a failure, of said cover).