Although I cannot find any knowledge base or support article about this bug, I did confirm there is a problem with Office Web Components version 9. OWC 9 ships with Office 2000. I recently closed a case with Microsoft Support which confirmed the bug. The only workaround is to use OWC 10 (XP) or OWC 11 (Office 2003).
I designed about 8 cubes, each with 3 to 6 time dimensions. Each time dimension needed a calendar date and fiscal date variant, so I would create the fiscal and calendar dimensions as a hierarchy of a dimension. In the Analysis Service wizard, you can do this by selecting the checkbox shown below.
If you do this for more than one “pair” of dimensions, only the first “pair” will display in the pivot table field list in OWC 9. The only fix seems to be to upgrade OWC. The dimensions do appear properly in the MMC cube browser, in Data Analyzer, and in later version of OWC.