I was wondering, who do you actually ask to take care of your business if you need to travel to see someone or do something important and you know you won't be online 12+ hours per day?
That is why you have employees.
If you're the President or the CEO of a company, you don't/won't really have time to deal with support requests from clients - you'll be working out how to get new clients, and what ways you can improve sales and have higher profits. You'll also be working out how you can cut costs, yet at the same time keep the same level of quality. You'll be doing a lot of things... and won't really have time to be dealing with clients requests: which is you should always have employees. That is of course if you're pretty large...
However, if you're not too large - and don't have enough money to pay employees, and so on, then you're could go to an outsource company. There are many individuals who are looking for some part-time work, and will be able to help you out - however, as the others above have said, you should always check them out thoroughly before you hire them.
As Vovex says, you cannot run your business by only checking e-mails and so on every 48 hours, it just doesn't work out. You need to check your e-mails all the time, and provide support in the hours you state. If you say you offer support between 9am and 5pm, then you need to offer support between those hours - not say 10pm till 11pm.
Also as Vovex says, be very careful about how much they charge. If you actually hire employees, you need to pay them an hourly wage as well as various benefits. Part-time employees also need to be paid by the hour, and so on. As he says, if you have someone who only wants $45 for the whole week (or even month), you can be sure that it won't be top-quality work.
Oh, and an outsource company you may want to check out is TouchSupport. They've some very good reviews at WHT, and also charge realistic prices. Their website is:
http://www.touchsupport.com/