JWcanada gave an excellent breakdown of the some of the critical areas in a BES environment. However i'm not sure you require a dedicated BES Admin....which is probably what your management is tryiny to say by their "push back".
A more likely approach would be to identify (or you may already have this in place) an escalation process to handle any issues that are BES related. Because the argument could be raised if, say your company went with another wireless solution (and sometimes they do things like that)...e.g GoodLink...(I'm not advertising...never even seen it). Would you require a GoodLink Admin?
An escalation process tied into your present ticket/incident handling system could serve to share the burden of support. For this to work, it would require that the front line support (HelpDesk) be trained to handle/resolve some of the basic issues as well as recognize those that would require an expert opinion/intervention.
The relevent areas to look at would be....
Server related- backups, upgrades, general maintenance (probably handled by server support)
Infrastructure related - partly server/network support
Handheld/Desktop related - should be handled by desktop support...even designate 1 or 2 individuals with the responsibility for user maintenance....e.g add/delete/modify users on the BES.
The key here is delegate...delegate...delegate. That would leave you more time to "explore" additional wireless technologies related to current environment.
Show management the different areas that are critical (see jwcanada post) and identify the addtional skillset required and if possible provide some "stats" on number of issues/tickets on per day or per week basis. They like to see numbers.
If that doesn't do the trick.....take two weeks off to the Bahamas..... remember to turn your wireless off...