That is so not fair. I don't believe these animal officers have that power to remove those dogs if there is no evidence of abuse no matter how many times they are called. Unfortunately, it may take many months, or even years in court to get that judgement, but by that time with your dogs away from you, the damage would have been done.

Find the complaining neighbor. Confront them. Ask them what their real problem is. Try to work though what bothers them as adults. But don't give in. In the end remind them that you, too, can file a complaint against them for making false accusations.