Hello Moonlit Aura,
Hopefully I can shed a little light on the subject.
You start with 4 chest available to be gained and they replenish once a week currently.
Key fragments have a chance to drop in a game that you win.
Chest are awarded if you or your teammates get an S- or better rating for that match.
You can only receive one per champion per season.
Example:
Game 1 You play Thresh and someone gets an S- or better rating, you get a chest for Thresh.
Game 2 You play Thresh and someone gets an S- or better rating, you do not get a chest as you already received one for Thresh.
Game 3 You play Sona and someone gets an S- or better rating, you get a chest for Sona.
Hopefully this clears it up a little bit. I'm on the boards for a little bit and can respond to further questions if I am notified.
Take Care!,
Piltover Customs
Edit: There was a Visual bug that it wouldn't show that you were awarded a chest even though you received one. If all the above is accurate for you and still not receiving, check to make sure it wasn't just a pop-up bug. If you are positive all the above was matched and you still didn't receive, write a support ticket in and they can look into it / fix things for you!