Once your press the stop button, the VI stops. It will no longer run code or react to buttons on the FP.
You simply need to keep the VI running without doing any acquisition. A state machine architecture would probably solve your problem. A finished VI should always run.
To clear the chart when the VI is stopped, right-click on in and select "Data operations...Clear Chart".
If you have LabVIEW 8.0, you probably could make an Xcontrol containing a chart and a "clear" button and it will work even if the VI is in edit mode.