It appears to be on some sort of cooldown. I've been playing with a group of friends and we've all been able to use each other's before they disappear. I'd guess it resets everyday but I can't say for sure yet.
I've used a friend more than once in a day, I've come to think the only usable Ally leaders are the ones with players online and of course I've noticed a cooldown of sorts but not at all close to a 24 hour one. Paying close attention I've noticed that some allies characters aren't usable at all at certain times of the day, whence I've not used them in that day of course, and aren't usable until the next day. Further supporting my "only online" theory. The cool down is a definite, as I've used certain allies in the same day more than once and was able to again in under 1 hour. Hope I helped.
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Add me, level 56