Is there some red tape reason you can't make a risk-based decision here to postpone without having to change "active"/"inactive" labels?
Also note that there may be more to auditing than just the product itself. Check for any other obligations that need to be maintained (e.g., even if they're not supplying product to you, as a key supplier they may still be required to notify your company of various changes and events, or to provide services and documentation, etc.).
Perhaps (depending on the real risks and stakes in the situation) you could scope out a cut-down or even remote audit just covering the relevant activities for the next period of time, and schedule the product-related half for a bit before you next expect to place an order. This demonstrates your continuing commitment to maintaining them as a key supplier whilst postponing the burden of auditing product-related processes. Keep QA happy with minimised audit requirements whilst maintaining the relationship from a management relationship perspective.