Wow, that's a bit disturbing that the strap breaks every time you've tried it...well, unless you have an abnormally massive head. <img src="/images/graemlins/wink.gif" alt="" /> Hey, I have a big head, so I feel like I can make "big head" jokes. <img src="/images/graemlins/smile.gif" alt="" />
But as figtree pointed out, you can staple beefier elastic from the fabric store to the edge of the mask as a replacement mask. If you already have a box of these masks and will keep them, you might want to store one of those tiny staplers and enough extra staples to fix all your masks. You can reuse the elastic between masks, although it won't cost much to buy extra elastic and keep that handy, too, particularly if you might be providing masks to other people.
Just wondering, but do these flat masks actually lie on your face at all, or do they puff out away from your face? I was just wondering if wrapping a bandana over the mask would work in a pinch when the strap broke. Well, that would likely mess up the seal on your face anyway, but still, it's probably better than nothing in an emergency, when you only needed protection long enough to leave an area.
Within the last week or so, I saw something in the news about some company being evacuated when an incoming payment envelope was found to contain a fine powder. Hazmat came to check it out. Turned out to be Kool-Aid or something like that, and was likely accidentally spilled into the envelope, but evacuating the office would be one situation where you'd only need protection for a limited time.