Unfortunately there is no easy resolution to this, and I think that in this case it may be a limitation of Outlook rather than MindManager.
Syncing between MindManager and Outlook is not as simple as it seems and occasionally some odd things happen. At the moment for example I can successfully send tasks from MM to Outlook and keep them synced, but while I can send tasks the other way from Outlook to MM, MM refuses to sync them and I get an error message.
I wrote a fairly detailed article about syncing between MM and Outlook a few years ago which I'll try to summarise here. Essentially there's a group of basic task elements such as start and due dates, priority and progress can be synced, edited at either end and resynced. This group also includes elements such as categories, topic notes and attachments.There's a second group which are not synced with Outlook, but are retained in MM. These include icons, tags (except Categories, which are synced), topic numbering, subtopics, callouts and hyperlinks. Duration is maintained and calculated at the MM only.
Unfortunately there's a third group of elements which are not only not synced with either Outlook or the dashboard maps, but are actually removed from MM maps by the syncing process. These include Topic properties, which are locked apart from Status, and Resources – indeed, once a task is synced, it becomes impossible to even add a resource to the same topic in MM.
As far as I can see the only option is to set up a separate Resources Tag group and use that to track resources in MM, bearing in mind that you can't see or edit this from Outlook. I tried to set up a SmartRule to write to Resources from a tag group or topic notes but the resources field in MM is completely locked by syncing.
My final words of advice are to test syncing carefully between MM and Outlook before setting up too many links, and be careful about things like changing the map location at the MM end.