I had my first (really long, 45 days) listing, and I thoroughly checked what i could after the listing on the damage since I was a bit skeptical that the guests are careless. Airbnb Host cover is valid if you report in 14 days, and absolutely does not care if there is something that is reported after that time interval.
In my case, the guest spilled liquid on a carpet placed on a wooden flooring, and then never attended it. I did not know if until I removed the carpet and found the flooring to be discoloured. Moreover, a nice metal artifact outside in the garden, used for decoration, was broken by the guest and quick fixed with glue. It later came off 40 days later, which is when I found it that the guests broke it.
Airbnb has to understand that some damages can't be assessed immediately, rather you find them out much later, specially if guests have done some quick fixes to them.