There is no problem with banning you, regardless of how much money you have spent on the account.
You have agreed to the Terms of Service, including:
"You further acknowledge and agree that you shall have no ownership or other property interest in your Account, and you acknowledge and agree that all rights in and to the Account are and shall forever be owned by and inure to the benefit of Riot Games."
"This License Agreement is effective until terminated. You may terminate this License Agreement at any time by notifying Riot Games of your intention
terminate. Riot Games may terminate this License Agreement at any time, for any reason or no reason. Upon termination, whether by you or Riot Games, the license granted to you in Section I shall immediately terminate, and you must immediately and permanently remove the Software from your computer’s permanent memory and destroy any and all copies of the Software that may be in your possession. "
"You also agree that Riot Games may change, modify, suspend, “nerf,” discontinue, or restrict your access to any features or parts of the Game at any time without notice or liability to you. You acknowledge that you have no interest, monetary or otherwise, in any feature of or content in the Software or the Game. "
You could hire an attorney and attempt to challenge the Terms of Service. Click Thru agreements are typically enforceable in the US. (http://en.wikipedia.org/wiki/Clickwrap#Legal_consequences_in_the_United_States)
However, if you were really gung-ho you have the legal right to challenge the TOS. This would require submitting yourself to binding arbitration. The cost of which would surely outstrip the value of your account.
Even if you won your case (highly unlikely), your recovery would be capped at the amount you had spent in the 6 months prior to the event that instigated the lawsuit. (Your banning.)
Best case scenario -- (also extremely unlikely) -- after probably a year or two of legal proceedings you win in Arbitration. You recover your attorney's fees and the amount you spent on your account in the 6 months prior to your banning. To do this, you have spent a large amount of time and money. (Although you will recover most of the attorney's fees, you still had to lay out that cash up front.) So you net the last 6 months of money you spent on your account. (Maybe a couple hundred dollars?)
If you lose -- the more likely scenario -- you would likely be on the hook for Riot's attorney's fees as well as those of your own counsel. (Probably close to $100k.)
Unless you're an eccentric billionaire with time and money to burn it makes no sense to pursue the case.