There are some zippers that can’t help but slide down and stay open. In cases like this, you can simply do any of the following:
Coat the teeth with clear nail varnish. This can give additional friction to overused zipper. Apply to a closed zip and it will glue the teeth together. You can do this once before wearing the problematic article of clothing.
Another short term solution to this problem is by using a safety pin to secur To secure the zip, just place the safety pin through the cloth just below the zipper pull and make sure you do it conspicuously enough so that it can’t be seen.
Last but not the least, you can always have the zipper replaced. You can bring your clothes to an alteration specialist or if you are thread-and-needle savvy, you can even do it yourself.