Ugh. There are much better solutions than keeping user funds in the hot wallet (fully cold storage with manual withdrawals, multi-signature wallets), but many "reputable" businesses STILL uses them. I don't understand why. If you want to store your customers funds online, do it the right way, or don't do it at all.
You cannot automate a cold-wallet scheme. Any automated website or tool will require a "hot wallet" of some kind. The more funds in the hot wallet, the longer the website / BTC Bank can go automatically. Customers like having funds available to them immediately... among other things.
I've seen fast food joints and parking lots with 24/7 attendants, it can't possibly cost more than $100,000 a year.