Test case randomly fails with "parent object was not found"

By the looks of it, you need to organise your mapped object correctly. Based on the following website http://secure.smartbearsoftware.com/samples/testcomplete15/dialogs/, I have defined the mapped objects as,

Parent

Property values that defines 'browser'

Property value that defines the webpage

Control

Dialog box within the control

Show alert link

You need to ensure that the structure of your mapped objects is correctly defined, and that it matches your webpage DOM (you seem to have two BrowserWindow beneath chrome?). Ensure that the mapped object property values are also correctly defined (the first xpath for AddWireButton is not correct XPath expression).

To instruct TestComplete on how to locate the objects in your tested application, name mappings must identify the objects correctly and uniquely.