Local support provides the perception of great control over the level of service. When service support is moved offshore (or anywhere outside your shop), it feels as if there is less control.
What can you do to maintain control over your offshore service?
Although it may seem as if you have less control, you may actually be able to gain more control over the level of service by establishing measurable and enforceable service-level agreements (SLAs) with your outsourcing provider. This will give you the control you need in order to ensure quality while still providing the cost savings afforded by offshore outsourcing.
Hold the provider accountable by including built-in financial penalties and rewards (this setup is sometimes even better than working with internal staff, where each person must be managed individually). The agreements should be fair for both parties. In other words, there should be financial rewards and risks for both of you.