This is a little vague. When you exit out of what? LabVIEW? When you quit LabVIEW the VISA sessions go away. Or when you exit your application? If so, LabVIEW is still running, so the VISA sessions are still in memory unless you explicitly closed them.
You said "I get the error out message of "Old VISA open in initialize.vi"". Are you sure you're getting an error message, or is the "source" element of the "error out" cluster simply set to this value with the "status" element set to false? If so, that's not an error message. If it's an actual error message what's the error code?
I also like to ask which version of VISA are you using. "Old" VISA Open should not be used if you've got a more recent version. Replace it with the regular VISA Open on your palette.
What error message do you get exactly? Also, as Dennis said, you should use the "regular" VISA Open. If you don't have the latest VISA driver for your Operating System, you can find an upgrade here.