When the Decomposition Tree in PerformancePoint is not "cool" - missing dimensions from decomp tree

In PerformancePoint, sometimes your users will see that a dimension goes missing from the selectable list when using the decomposition tree - and indeed, from the entire Analytic Chart (or grid)

To replicate this behaviour, create a new Analytic chart against the Adventure Works Database, with Internet Sales Amount as the measure, Product Categories as the bottom axis, and Customer Geography as the background.

Create a filter based on customer geography, and make it a multi-select tree. Make the default the All member.

Create a new dashboard, add these two components, and connect them à Customer Geography Unique Name to Customer Geography on the report. The deployed page will look like this:

Figure 1

Choose the decomposition tree, and customer is available. Great.

Figure 2

Change the selection in the filter to be Australia and Canada, and go back to the decomp tree

Figure 3

The explanation is actually very simple. PerformancePoint builds the decomposition tree directly as a traversal of the AS hierarchies. In order to build a decomp tree based on a multi-member select, it would have to have a whole calculation engine similar in scope to the AS Formula Engine, and this would be a performance hit.
Solution: Fix your dimension model. You should be querying at a member level, not summing multi-selects (well to do decomp, anyway)

I'm being facetious, this is horrible behaviour.

Also, this won’t happen if the member is on the axis  ~ as the user can only ever click on a single member in the chart