I asked this question last night at 11:00 and received my daily "random treasure" from the man in the black suit and saved my game there.
This morning at about 6:30, I talked to him again and he gave me another random treasure.
Same with the Nimbasa city sports dome trainers; I was able to fight them again, although some of the trainers changed.
I believe it resets upon certain conditions or something, but I know what you mean.
Sometimes I wait a full 24 hours and I'm still not able to do any of the dailies!
(Like how the props guy hasn't given me props in months!)