I can suggest three advantages:
1. Simplified configuration for the hosting company
2. Eliminates the possibility of SE bans due to the actions of another virtual account sharing the same IP
3. May avoid future problems
The W3C upgraded the HTML 1.0 spec to 1.1 a few years ago. The upgrade included a provision for virtual hosting. Browsers, servers, and spiders all needed to upgrade to support it. Hence, there was a transition period when virtual hosting was "controversial," with some having generally good experiences and while others lost traffic and SE rankings, etc.
Simplified configuration for the hosting company
Most hosts occasionally reconfigure their boxes as their business grows and changes. This is supposed to be transparent to web site visitors but often is not. Virtual hosting is a much more complex configuration for a host to maintain and is more error prone during these changes. One of the more common reasons for a virtually hosted site to be down is a misconfiguration of virtual hosting parameters.
Eliminates the possibility of SE bans due to the actions of another virtual account sharing the same IP
Rumors still abound that SEs may ban an IP (not simply a domain name) for major infractions. Personally, I don't believe that's correct presently, but do you want your client to test the validity of those rumors?
May avoid future problems
In the past, a dedicated IP was cheap insurance against virtual hosting configuration problems. The expanded IP numbering system, IPV6, will be deployed soon. It may create some issues with virtual hosting or virtual hosting configurations. A dedicated IP will probably avoid most of these.