Firstly to answer one question in the PDF file: "I’m not sure why the role only sees SAP_Asset_CapitalizationData and the form shows SAP_Asset_CapitalizationData1 but it appears to be correct. "
I am assuming you have eliminated the possibility that the 'to do list' role is not available when the form reopens immediately after the first action, and after subsequent actions will not be updated if the form reopens automatically.
On the form you are seeing an 'instance' of the process business object. As such it is named after the object with a '1' added. A second instance would have a '2' added, etc. In the role calculation, as anywhere else in the process itself, you will refer to the process business object by the object name itself. I'll not try to explain exactly why as it gets too far into OO for this issue.
I myself would examine the actual data for the folder. We have a form in our library (see link below) that shows all variables and their values for a Folder. It is only visible to admin, so we add it to every stage in every process. We also add a form showing the current status and another showing Designer Log errors. Together, I suspect these may help with the issue.
Given these forms, I would check the To Do list values on the status form, the actual variable values in the Variables form, and then see if there are any Designer Log entries on the Designer Log form. Something gone awry, that is clear, because this works all the time for us.
