Hextech Keys?

So uh.. How do I obtain these without purchasing them for RP?

I recently returned after a 10ish month break(My daughter was born, and I just couldn't be sure I'd have an hour+ To sit and play, so I stopped playing until she was more predictable.), and discovered this hextech system. Nifty!

Now.. The problem. The first week I got 4 boxes, and 4 Keys. It took me slightly longer to get the keys than the boxes, but that's fine. My problem is that SINCE then I have gotten 3 boxes(One per week as they've become available), but I haven't gotten even one single key fragment, I understand that they're only available for wins, and I've read that they have a drop curve, getting more rare and resetting.. But it's been several weeks since I've gotten even one fragment, and I now have 3 boxes saved up without keys for them. At this rate I'll end up with a lot of boxes, but no keys.

Is there ANYTHING I can do to obtain them other than get RP? Does it reset a month after I got my first key, and thereby one week a month I'll just get the 4 keys for that month? At this point I'm starting to think I'm just going to have an abundance of boxes, because 2-3 weeks without even one key shard seems like the drop is just plain disabled for me at this point.