We have never outsourced and probably never will. I have had a partner twice in business and it's always a BAD idea, the 2 times it happened, it's forced me to close my businesses, because of one reason or another. I've now started fresh with a new business venture, a new outlook and I'm on a roll, all on my own, atleast for a while.
You just can't find anyone that is trustworthy or dependable, as something is going to happen and they are going to mess you up in one way or another.
Don't outsource your support, provide support to your own customers. If you can't do 24/7/365 support, offer support during set hours for your customers and let them know when you will be responding to tickets, live chat and phone calls or however you offer your support.