I used to put all our inset puzzles in a bag and I hate it when the puzzle pieces fall out. I have a few bags of puzzles and it takes some time it takes some time to locate the pieces when you have a few in a bag. I make sure no puzzle pieces go missing. I'm not a neat freak but I'm very particular when it comes to the kids' toys. I hate it when I see kids throwing the toys into the toy bin. So, I never have one. All their toys are placed on shelves. I hope they can learn to take care of their toys and to appreciate what they have. If a toy goes missing, the whole family join in the search. I'm proud to say we have not lost any toys so far, the few times we couldn't locate them was because my domestic helper kept them at some obscure places by mistake or it went real deep under the bed.
Ok, back to the puzzles. I now keep each puzzle in individual plastic bags (yeah... I know, it's not environmental friendly but I doubt I will ever find the time to sew fabric ones), those that are slightly bigger than A4 size will fit most standard sized puzzles, like those from Melissa & Doug. (we have lots of those) So, it's easy for me and them to just pick up the puzzle and all the puzzle pieces will be contained in that bag. Once we are done with it, we just put it back. It has been working great. I got my plastic bags from SKP. I chose those that have a resealable seal. It's not expensive, few dollars for a hundred pieces and I have been using the bags for many other purposes too, like storing their artworks.