If by “air integrity” failures you mean noncompliance to whole package integrity tests such as ASTM F 2096, “Detecting Gross Leaks in Medical Packaging by Internal Pressurization (Bubble Test) then the AQL level is accept on zero failures. Sterile barrier integrity, as measured via physical integrity, is a critical defect and no integrity failures are permissible. Additionally, sterile barrier system package validations should have as part of the protocol, a statistical rationale for the selected sample size. Regardless of the sample size the physical integrity acceptance criterion is zero defects. Another note to consider is that each individual medical device manufacturer should have a risk assessment on file for their manufactured products. There are no industry standards for risk, however, breach of sterile barrier integrity is universally considered a critical defect, relative to AQL levels.

I am making an assumption here, but if you are referring to integrity failures found as part of a set of manufacturing release criteria and if a defect is found, then a typical QA response is to determine root cause and examine packages produced prior and after the date of manufacture to determine the cause and extent of the failures, and make all prudent and required corrective actions.

Are you referring to air permeance through your porous Paper substrate?   As you have a porous substrate—Paper, there is a normative reference (hard requirement) for resistance of impermeable materials to the passage of air (Annex C) of ISO 11607. Impermeable materials for sterile barrier systems shall be tested for air permeance in accordance with ISO 5636-5. Test criterion: After not less than 1 hours, there shall be no visible movement of the cylinder, within the tolerance of +1 mm.

If I have misunderstood your question, please provide additional clarifying information.