How To Destroy This Beam After Magnitude is Higher?

Okay so I think i found the issue, but i can't be 100% sure since I can't reproduce Your exact circumstances. I took the liberty of tidying your code a bit, only after that, I have found the issue.

--I added this line for clarity, should also improve performance a bit
local player = game:GetService("Players").LocalPlayer
local character
local root 
while wait() do

	character = player.Character or player.CharacterAdded:Wait()
	root = character.HumanoidRootPart

	for i,v in pairs(game.Workspace.Beams:GetChildren()) do
	
		local mag = (v.Position - root.Position).magnitude
		if mag <= 12 then
			if v.Ready.Value == true then
				if character:FindFirstChild("LookinBeam") == nil then
					local beam = script.Beam:Clone()
					beam.Name = "LookinBeam"
					beam.Attachment0 = v.Attachment
					beam.Attachment1 = root.RootRigAttachment
					beam.Parent = character --always parent parts last
				end
			end
			--below if statement is inside mag<=12 statement, you need to move one "end" around
		end --end should be here

		if mag >=13 and character:FindFirstChild("LookinBeam") then
			character.LookinBeam:Destroy()
		end
		-- end -- this end has been moved
	end
end

So guys - remove clutter a bit, make proper spaces for statements, etc. Then you can find errors easily. Have a nice scripting session.