Here is a brief discussion of a number of elements of an informed decision on email outsourcing. These are not all of the elements you should consider, but it's an excellent place to start, and will place you in a much better position when it comes time to make the final determination on the necessity or cost effectiveness of outsourcing.
Efficient Human Resource Deployment
How many IT staff do you have? How much of their time is devoted to the mundane problems with email and connectivity trouble? If your business is like most businesses, the answers are "very few" and "too much" —in that order. Most IT departments are overrun with requests for help on email-related issues, and what few resources your IT staff has will be misdirected to issues that could be solved by outsourcing. When outsourcing becomes a reality for your company, that same staff, should you decide to retain them, will be able to focus their efforts on more complex and vexing problems, or develop new approaches to streamline the technology resources the company will choose to keep, rather than outsource.