I love my Easypay Metrocard.
They definitely suspend accounts if a replenishment attempt is declined and you don't have a valid backup payment method. So it's important to always have a backup credit card linked to your account AND to keep the expiration date of the backup card updated. My wife experienced exactly the same thing as gfunkdave when her TransitChek debit card had insufficient funds and I neglected to keep current the expiration date of the backup credit card on her EasyPay account.
It WOULD be nice if they sent you an e-mail letting you know your account had been suspended and explaining why, though.
But overall the Easypay cards are incredibly convenient, as I never have to worry about whether I have a sufficient balance on my card (or my wife's card or our nanny's card). And if I lose it, a simple e-mail to EasyPay customer service will immediately put a hold on the old metrocard and transfer the balance to a new one. It takes about a month to get the new card, but it's still better than losing a regular pay-per-ride card, where you'll never get the balance back.
So yeah, it's not perfect, but I still think it's way better than the available alternatives, especially if you're a pay-per-ride user (if I was an unlimited user I might be more reluctant to get EasyPay, since you can't "time" when you start your month).