After the player dies, the script stops working?

First of all, I'm not sure why you'd want to check to see if the player is touching a button every single render step. It is much more efficient to keep a list of each key's state and update them when each key is pressed or released.

Secondly, I'd try using :Move() instead of :MoveTo(). :Move() will make the player move in the given direction, and comes equipped with a bool for if the movement should be relative to the camera or not.

Lastly the reason your code stops working is because when the character dies, game.Player.LocalPlayer.Character is nil for a bit while you respawn. This makes an error pop in your script.

The following Code is an example of what I would possibly do in order to accomplish what you are trying to. Note however the initiation of the Character variable will no longer be valid upon the first respawn and the gameProcessed variable simply means the player's focus is on the game (not chatting or typing in a textbox, etc).

Leave a comment if you need anything explained further.

local UserInputService = game:GetService("UserInputService")
local Character = game.Players.LocalPlayer.Character
local Keys = {}

function UpdateMovement()
	local forwards = Keys[Enum.KeyCode.W] or Keys[Enum.KeyCode.Up] and true or false
	local backwards = Keys[Enum.KeyCode.S] or Keys[Enum.KeyCode.Down] and not forwards and true or false
	local left = Keys[Enum.KeyCode.A] or Keys[Enum.KeyCode.Left] and true or false
	local right = Keys[Enum.KeyCode.D] or Keys[Enum.KeyCode.Right] and not left and true or false
	local xMovement = left and -1 or right and 1 or 0
	local zMovement = forwards and -1 or backwards and 1 or 0
	Character.Humanoid:Move(Vector3.new(xMovement, 0, zMovement), false)
end

UserInputService.InputBegan:connect(function(input, gameProcessed)
	if input.UserInputType == Enum.UserInputType.Keyboard and not gameProcessed then
		Keys[input.KeyCode] = true
		UpdateMovement()
	end
end)

UserInputService.InputEnded:connect(function(input, gameProcessed)
	if input.UserInputType == Enum.UserInputType.Keyboard then
		Keys[input.KeyCode] = false
		UpdateMovement()
	end
end)

Reinitalize

The easiest way to do this is to disable then re-enable the control script forcing it to restart.

Server Script

game.Players.PlayerAdded:connect(function(player)
	player.CharacterAdded:connect(function(character)
		CONTROLSCRIPTLOCATION.Enabled = true
		character.Humanoid.Died:connect(function()
			CONTROLSCRIPTLOCATION.Enabled = false
			character.Humanoid.Died:disconnect()
		end)
	end)
end)