I was just playing Vayne and had some massive, massive drops in FPS and got the "Attempting to Reconnect". I had to disconnect and then reconnect, it helped, but not a lot. I felt awful because I know I cost the game for my team.
Select lines from dxdiag:
Processor: Intel(R) Core(TM) i5-2500K CPU @ 3.30GHz (4 CPUs), ~3.3GHz
Memory: 8192MB RAM
Card name: NVIDIA GeForce GTX 570
Display Memory: 4049 MB
Dedicated Memory: 1233 MB
Shared Memory: 2816 MB
Let me know if you need any other details! Thank you Dannamoth.