Hello,
The default behavior of the debugger is to auto-run to a label on program load. The default label is 'main'. So if you program has a 'main', it will run to it and then halt. If it does not, it will just continue to run until some breakpoint is encountered. You can disable this behavior (or change the label to run to) by changing the debugger properties.
There is a DSS APIs to change the debugger properties. See the below wiki topic on how to do this:
http://processors.wiki.ti.com/index.php/Debug_Server_Scripting#Debugger_Properties
Try this first. Strange scenario you describe later I'm not sure what is going on. Hopefully changing the debugger options will help.
thanks
ki