I've searched the internet, and it seems that the only thing that causes ORAS's in game clock to freeze is changing the time. (Which can be done a few ways, such as changing to a 3DS that doesn't have the same time as the 3DS the game was last played in.)
So, the problems could have been:
- You or somebody did change the time and you didn't remember/realize
- There was a glitch
- The thing below
To get Mirage Spots, you need to connect your game to the internet. (Excluding the ones you get at the beginning of every day before connecting to the internet.) That could have been your problem, you didn't connect to the internet before you went looking for your Mirage Spots. In other words, there was no problem with the clock, you just might not have connected to the internet.
Those were the only things that I could find/think of.
Hope this helps!