Can you explain why can't pyramid investment scheme succeed in the long run?

I have a thinking that since most if not all the pyramid investment schemes follow a compand base in their bonus or interest payout to their investors and that base reguires a very hardwork in recruitment of new investors as to keep the balance of payout to old investors, in short it is hard to maintain the compand base of bonus and interest to all investors well there are no new recruits who well refresh the cash inflow to balance.