Hi Victoria,
"the corresponding object must be present in the system" means that not only the final object must be present (i.e. visible), but all its parent objects must exist as well.
TestComplete notes in the message box what parent object is missing after the "Missing object:" phrase.
Missed object may seem to exist for you, but you must carefully examine and compare the value of the properties specified in the NameMapping editor for the problematic object with the values shown in the Object Browser. For the web sites with dynamic web pages, the objects hierarchy may seem to be stable from run to run, but the objects itself may have different identifiers - i.e. tableA157R7 may become tableA157R18.
In this case you should either find a set of stable properties to identify the given object uniqely and stably, or consider using the Extended Search (
http://support.smartbear.com/viewarticle/55674/).