Thank you for your patience; unfortunately there is no statute of limitations that governs this; I have reviewed the statutes in detail (located here) and this issue is not addressed.
Statute of limitations apply to civil proceedings (as opposed to special proceedings).
This is discussed at great length here
The reasoning behind it is that the city does not have the manpower to enforce the ordinances (ie to police the entire city for violations, especially since many of them are located inside private homes) and so that once the city becomes aware of it (either by happenstance or by a report) they can address it at that time.
I am sorry that this is the case as I'm sure that is not the information you were looking for but I have a moral obligation to provide accurate information.
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Information provided is for educational purposes only. Consultation with a personal attorney is always recommended so your particular facts may be considered. Thank you and take care.