Establishing a Web presence means more than just throwing up a server and letting it run. To be a Web-enabled company, you have to adopt Internet time, and that may mean changing your operational model. The Internet is a 24x365 operation, and when you invite customers to do business with you on the 'net you will be expected to become 24x365 yourself. The medium sets expectations.
That means that vomiting up an error code at midnight on Sunday, telling the customer to call support, and then responding with a recording which says that support is only available weekdays from 0800-2000 is not good enough; you will only make customers angrier than they already are. Your tech support should be reachable whenever your website is reachable, or you are making trouble for yourself.
Sorry. I realize this will increase your operating costs by a few thousandths of a percent. But it's true. The business office can keep business hours (though you would do well to adapt to 'round-the-clock operation there as well) but there must be someone reachable all the time. You told your customers you would be there for them when you set up your server and invited them to use it. The benefits you get from a web site are not free.