That was a problem with those old Mirros. I had three teens using the ones I had and the tops wouldn't stay on
so I drilled holes in each side and use little 1/4 inch sheet metal screws to hold them on, starting with the smallest I could find. After a while the soft aluminum would enlarge so I would go to a larger diameter screw.
This worked just fine for the few year the kids wanted to do that. The things are cheap but they do the job.
I haven't made press cookies for a few years but I still have several presses.
The last time I used a cordless, battery operated one.