Why do multiple loops inside a script seem to fail when other loops are running?

Probably because you're using endless loops and not putting coroutines

Say you have this in a script;

while wait(1) do
    print(math.random(1,5))
end

print('Derp')

'Derp' will never be printed, due to the endless loop above it.

So a way to fix? Coroutines.

coroutine.wrap(function()
    while wait(1) do
        print(math.random(1,5))
    end
end)()

print('Derp')