I honestly believe both the question and the answer are mistaken. There's no part in the trick house that indicates a necessity for an active internal clock.
The original asker made an incorrect assumption about it being clock based, but in reality I'm pretty sure it was not 'updated' because either s/he finished all the challenges or didn't complete the next gym. It's not hard to visualise the latter, because if s/he did like 3-4 gyms and then tried each trick house challenge after an arbitrary time gap, the change could be attributed to being a function of time as opposed to it being a function of the number of badges you owned, which is what current knowledge of the game indicates.
Finally, my playthrough of Emerald happened with a dry internal battery and my clock didn't work. However, as I recall, I was able to complete the Trick Master's challenges.
Source: Personal Experience.