By suspending your listings and not explaining the reasons, Airbnb paced itself in violation of its own Terms of Service, specifically:
5.3 Independence of Hosts. Your relationship with Airbnb is that of an independent individual or entity and not an employee, agent, joint venturer, or partner of Airbnb, except that Airbnb Payments acts as a payment collection agent as described in the Payments Terms. Airbnb does not direct or control your Host Service, and you agree that you have complete discretion whether and when to provide Host Services, and at what price and on what terms to offer them.
13.3 Member Violations
...For minor violations or where otherwise appropriate as Airbnb determines in its sole discretion, you will be given notice of any intended measure by Airbnb and an opportunity to resolve the issue
Based on what you described, you have not been provided any information or an opportunity to resolve the issue. If there is no any traction, your best bet is the arbitration, especially if the losses are sustained. Having said that, please be aware that if AIrbnb sees that the company is at fault, they request the assigned arbitratior to order the court proceedings with the hope that the costs and loss of time by a host will serve as a strong deterrent to have a matter decided in court. Sneaky strategy that apparently works...