The way key fragments work is, when you receive a key fragment, the drop rate for the next one is reduced, and once you receive that key fragment, the drop rate for the next one is reduced even further. This continues every time you receive a key fragment. The drop rates for key fragments do reset, though, about 1 month after you receive your first key fragment.
So, for example, lets say the first key fragment you received when the system was first released was on March 24th. Every time you receive another key fragment, the next one will have a lower drop rate. Then, once April 24th comes around, the drop rate will reset back to normal, and the cycle will start over again. Each key fragment you get will lower the drop rate of the next one, and the drop rate will reset once again approximately 1 month after you receive your first key fragment since the last time it reset.
Now, as far as how the reset in the drop rates work, I'm not 100% sure about that. According to this Rioter post as well as the second Riot post in that thread, we know that drop rates do reset on a monthly basis, but they say that it's on a per player basis. So it won't reset for everyone at the same time, the drop rates will reset at different times for each player. From this, I'm drawing the conclusion that once you receive your first key fragment, the drop rate will reset 1 month after that date, and then once that reset happens, the next reset will happen 1 month after you receive your next key fragment, and so on and so on.
Hopefully this helps and makes sense, I know that I'm not always good at explaining things.