@Kathleen710 Officially, there's not a published limit to the number of claims a host can initiate. But every time you request compensation, your listing probably gets internally flagged as a potential problem. If the claims are deemed excessive or unreasonable, that could result in de-listing, suspension, or suppression in the search results. But they don't disclose the reason behind these actions, so hosts can only speculate.
The AirCover isn't all it's cracked up to be, so I suggest taking every measure you can to avoid needing it. That means furnishings that are affordable to repair or replace, and a portion of your earnings set aside as a fund for handling minor breakages and routine maintenance. A private home insurance with STR coverage is also essential for whole-house rentals, and AirCover is no substitute.