I too have need for this feature, and I am upset to learn that it is not possible in the current version. It seems like the easiest way to provide this is to allow the log to be cleared from scripts. Then I can run a group of tests, export log results, clear the log and then run the next group of tests and repeat.
Right now we have the same problem where logs are extremely slow to view (MHT) outside of TestComplete. I am considering the idea of writing a custom tool to drive TestExecute so that I can get separate logs.
At any rate, please add me to this request.