My internet is pretty fast but in league i get over 500 ping

Dear Riot When I start the game it works perfectly (I usually get about 50 ping), then 5-10 minutes pass, I will get hit with this big message at the top of my screen saying, attempting to reconnect, then if it eventually does go away I will still end up getting 500 ping and it is impossible to play. I try and disconnect them comeback but it always does the same thing, attempting to reconnect. when I play a custom game myself or go in to training tool it works fine or if I am playing a different game it works perfectly . if you know how to fix it or if you had the same problem before please tell me because I love league and this is making it impossible to play. Plz help

Sincerely AshTheFlash04