There does appear to be a problem with handling COBOL files within a web application when rununits are in effect.
I wrote a demo program here that defines files within the web aspx.cbl program and it works fine even when called multiple times. As soon as I create a new rununit and even after calling its StopRun method, I see the error that you are experiencing on the second call.
Even if I move the file handling to a separate class and invoke it from the web page I run into an exception if rununits are being used.
Please create a support incident with Customer Care and reference my name in the description so that it will be routed to me.
Thanks.