In Arizona, how long before I can consider my rental property abandon??

There is information at this link

Arizona Revised Statutes §33-1370  Abandonment; notice; remedies; personal property; definition - Arizona Arizona Revised Statutes §33-1370  Abandonment; notice; remedies; personal property; definition - Arizona Code :: Justia (http://law.justia.com/arizona/codes/title33/01370.html)

According to subsection H in the link provided in your first response, it can be anywhere from 5-10 days depending on circumstances.

Do you live at or near the property? You would have to make frequent checks to make sure the tenant has not been using the property.