How do I make Jump Power not reset on death?

Improvements

Use :WaitForChild() to make sure a part exists before referencing it in your code

Use :GetService() for the Players Service

It's better for your game's RAM to set the parent of a new instance after its properties are set

Issues

For "prest" the "onServerEvent" should be capitalized to OnServerEvent (Lua is case sensitive)

OnServerEvent should occur outside of the Players' PlayerAdded function

CharacterAdded should not be called by the Died event, if anything, the Died event would be called from the CharacterAdded event as the current character would be referenced. This is because the Died event fires in relation with the removal of a character, and would be unable to reference the new character.

In the "prest" server event, you have the jumppower value set twice, this may be intentional, but the final output will be the last one (I've dashed out the first setting of the value as the rest of the code doesn't seem to need to reference it.

If the Humanoid's JumpPower is supposed to be based on the JumpPower number value, you may want to add the following:

JumpPower:GetPropertyChangedSignal("Value"):Connect(function()
    player.Character:WaitForChild("Humanoid").JumpPower = JumpPower.Value
end)

inside the PlayerAdded function after the creation of the "JumpPower" variable

Revised Server Script #1

local prest = workspace:WaitForChild("Prestige")
local close = workspace:WaitForChild("Close")

game:GetService("Players").PlayerAdded:Connect(function(player)
    local leaderstats = Instance.new("Model")
    leaderstats.Name = "leaderstats"
    leaderstats.Parent = player

    local reb = Instance.new("IntValue")
    reb.Name = "Rebirths"
    reb.Value = 0
    reb.Parent = leaderstats

    local costmult = Instance.new("IntValue")
    costmult.Name = "costmult"
    costmult.Value = 1
    costmult.Parent = player

    local JumpPower = Instance.new("NumberValue")
    JumpPower.Name = "Score"
    JumpPower.Value = 0 
    JumpPower.Parent = leaderstats

    player.CharacterAdded:Connect(function(char)
        local hum = char:WaitForChild("Humanoid")
        hum:GetPropertyChangedSignal("JumpPower"):Connect(function()
            JumpPower.Value = math.floor(((hum.JumpPower * 20) - 1000) + 0.5)  
        end)

        hum.JumpPower = (JumpPower.Value / 20) + (0.05 * (reb.Value + 1)) + 49.95
    end)
end)

prest.OnServerEvent:Connect(function(plr)
    local costmult = plr:WaitForChild("costmult")
    local reb = plr:WaitForChild("leaderstats"):WaitForChild("Rebirths")
    local JumpPower = plr:WaitForChild("leaderstats"):WaitForChild("Score")
    local hum = plr.Character:WaitForChild("Humanoid")
    print(costmult)

    if JumpPower.Value >= (1500 * costmult.Value) then
        close:FireClient(plr)
        hum.JumpPower = 50
        -- JumpPower.Value = JumpPower.Value - (1500 * costmult.Value)
        reb.Value = reb.Value + 1
        costmult.Value = costmult.Value * 2
        JumpPower.Value = math.floor(((hum.JumpPower * 20) - 1000) + 0.5)
    end
end)

Revised Server Script #2

local ReplicatedStorage = game:GetService("ReplicatedStorage")

ReplicatedStorage:WaitForChild("RemoteEvent").OnServerEvent:Connect(function(player)
    local hum = player.Character:WaitForChild("Humanoid")
    local reb = player:WaitForChild("leaderstats"):WaitForChild("Rebirths")
    local costmult = player:WaitForChild("costmult")

    hum.JumpPower = (hum.JumpPower + (0.05 * (reb.Value + 1)))
    print(costmult.Value)
end)