Support found that the Pledge in question was set to a Pledge Status of “PC”, for Partially Collected. The PC pledge status is used when some payments have been made on it, but it has not been fulfilled and you do not expect to getting any more payments for it. So, the program is not finding active open pledges, so it is not bringing up a list of pledges to select from.
To fix the issue, change the Pledge Status back to “PF”, which you should be able to do from the Giving History Detail screen for the PL in question and then zooming in on the Pledge Number field to access Pledge Information. Once you have changed it back to PF, you will be able to add the Pledge Payment again and the Pledge will pop up.