I was having the same problem and found a solution - hopefully it helps others. The issue was with the assignment of Organizational Area in the Class I was trying to assign to the Object.
When creating my Class I'd assigned it to Organizational Area L (Linear Functional Location) on the Basic Data tab, but what I'd missed is assigning the same Organizational Area to the Characteristics on the Char Tab. Each entry on this tab seems to need to be assigned the Org Area L in the appropriate column of the grid.
After adding this value I was able to select my Characteristic in the Linear Data tab of the Functional Location. It should be noted that as previously mentioned, you do still need to assign the Class at the Functional Location level in the standard way and any Characteristics you want to use in the Linear tab must be assigned as values in the standard screen.