Why doesn't my leader board script work after a player dies?

First of all, you will not reach that second "PlayerAdded" event because "alive" is never changed and so that loop you have there will run forever without stopping. Considering you were already in a "PlayerAdded" event a second one was not required. In the player object there is an event for detecting when the character model spawns. I.E when the player is "alive"

I believe that something like this was what you were looking for:

--script by Legobrain9275--
local alive = true
game.Players.PlayerAdded:connect(function(player)
    local stats = Instance.new("IntValue", player)
    stats.Name = "leaderstats"
    local timealive = Instance.new("IntValue", stats)
    timealive.Name = "TimeAlive"
    local xp = Instance.new("IntValue", stats)
    xp.Name = "XP"
    local level = Instance.new("IntValue", stats)
    level.Name = "Level"
    player.CharacterAdded:connect(function(character) --Detects when the player respawns, perfect time to set alive to true
        alive = true
        character:WaitForChild("Humanoid").Died:connect(function() --The WaitForChild returns the instance of the humanoid
            alive = false
            player.leaderstats.XP.Value = player.leaderstats.XP.Value + (player.leaderstats.TimeAlive.Value/10)
            player.leaderstats.TimeAlive.Value = 0
        end)
    end)
    while true do --Make sure this loop runs forever
        if alive then player.leaderstats.TimeAlive.Value = player.leaderstats.TimeAlive.Value + 1 end
        if player.leaderstats.XP.Value >= 1000 then
            player.leaderstats.Level.Value = player.leaderstats.Level.Value +1
            player.leaderstats.XP.Value = 0
        end
        wait(1)
    end
end)

Hope this helps and works (I have tested and it does work for me)

Your script never makes it past line 22.

    while alive == true do --This script goes on forever, and never allows you to move on
        wait(1)
        player.leaderstats.TimeAlive.Value = player.leaderstats.TimeAlive.Value + 1
    end

In order to allow the script to go past that loop, you can use a spawn() function to execute the loop on another thread.

spawn( function()
    while alive == true do --This script goes on forever, and never allows you to move on
        wait(1)
        player.leaderstats.TimeAlive.Value = player.leaderstats.TimeAlive.Value + 1
    end
end)

Also, on line 24, I believe you were trying to connect to the event player.CharacterAdded. List of Player events here.

Also, a few other things.

Line 18 while alive == true do will run as long as the player is alive, however, once the player dies, it will stop running.

Also, b.Character:GetPlayerFromCharacter(c)doesn't make sense, because we already have the player defined as player.

Additionally, on line 34, this code: if player.leaderstats.XP.Value >= 1000 then only runs once.

And, instead of using a Humaniod.Died event, we could use CharacterRemoving

--script by Legobrain9275--

local alive = true


game.Players.PlayerAdded:connect(function(player)
    stats = Instance.new("IntValue", player)
    stats.Name = "leaderstats"

    timealive = Instance.new("IntValue", stats)
    timealive.Name = "TimeAlive"

    xp = Instance.new("IntValue", stats)
    xp.Name = "XP"

    level = Instance.new("IntValue", stats)
    level.Name = "Level"

    spawn( function()
        while true do
            wait(1)
            if alive then
                player.leaderstats.TimeAlive.Value = player.leaderstats.TimeAlive.Value + 1

                if player.leaderstats.XP.Value >= 1000 then

                    player.leaderstats.Level.Value = player.leaderstats.Level.Value + 1

                    player.leaderstats.XP.Value = 0
                end

            end
        end
    end)

    player.CharacterAdded:connect(function(b)
        alive = true
    end)

    player.CharacterRemoving:connect(function(b)
        alive = false
        player.leaderstats.XP.Value = (player.leaderstats.XP.Value + (player.leaderstats.TimeAlive.Value/10))
        player.leaderstats.TimeAlive.Value = 0
    end)


end)