Yes, each time you print or file W-2's - or any payroll tax form - for a period the local saved file is replaced. If you don't want that to happen, then open the saved file and print from there.
Note that each time you create W-2's and other tax forms, QB pulls your payroll data as is currently exists and uses the current form image and code to create the form, and so it's somewhat likely that you won't get the same results you did the first time, especially years later. So, doing that is suspect to begin with, which is why QB puts up warnings to this effect in some cases.
Also, in this particular case 1) you're not required to provide the employee another W-2, and instead can refer them to the SSS to get a copy of what you filed, and 2) You can elect to provide the employee only with your company copy (that is filed with the SSA) , which you can do by opening the saved PDF and printing just that page.
