Your grades have nothing to do with getting fragment drops, just premade size, and you need to win to get fragments.
The drop rate lowers with each fragment you get during a ~30 day period, so near your drop rate reset you'll get fragments almost every win as you get the 'easy' fragments, but once you start getting to 10+ fragments you can win literally dozens of games without a fragment since the drop rate is so low. This has a side effect of making fragment seem super rare for awhile if you manage to get most of your fragments early on.
I'm sitting on around 4-5 boxes have never missed an S rank chest so far, with no fragments. The drop rate for fragments is probably good enough for most people to manage 2-3 keys a month, and while 4 is theoretically possible, anyone who is getting a weekly S chest is probably going to eventually end up with a surplus of chests compared to keys.
Those who don't manage a weekly S rank chest are prone to eventually have the opposite problem.