Please provide more information. It sounds like you think the tests are running too slow. Is it the execution of the individual test scripts that you think is too slow, or how long it takes between the end of one script and the beginning of the next?
Whether or not QTP remains open after executing the last test is a setting in the QTP Remote Agent application on the system where QTP runs. There is a checkbox in the Remote Agent Settings labeled "Keep Quick Test open after a Test Lab run session ends" Try unchecking that.
There is also a setting for "Restart testing tool after # Runs". You might want to check the setting on that also.