After some further investigation I have learned the following:
The dimension that the Variable is based upon is not refreshing.
Here is exactly what is happening:
1. When I open the report I notice that there are some items in the dimensions list that are in bold font. It appears that these are not updated.
2. When I refresh the report the input control goes away and the dimension is not refreshed.
3. I add the dimension as a table anywhere in the report and it says #REFRESH
4. I refresh the data and the information shows in the table, at the same time my input controls appear. I then delete that report table.
5. I save the report and exit out of it.
6. Reopen the report and input controls are showing
7. Refresh the report and the input controls disappear and it appears I need to refresh the dimension again.
8. If I add the table with the dimension values back, and refresh, the values appear and the input control appears.
9. If I save the report, close it out, and open it back up without deleting the table with the variable data and refresh, the input control stays.
So it appears that for some reason, it is not refreshing without it being on a table or something in the report.