"The object does not exist" even though mapping seems right

We need to see screenshots of your object tree for the application, code or KWT examples, and what your name mapping looks like. More than likely because you are just recording the test and letting the object be mapped automatically, you are not providing a good criteria for your mapped objects.

Recording and automatic name mapping is great for a starting point, or figuring out what objects you need, but will never be reliable on it's own. You MUST go in and update your identification properties to something reliable.