This is a headset issue. When the agent's use headsets and the headset button is active there is a quasi-connection to the switch that allows the work code to be entered.
Try this...
On the 4620 phone, after an ACD Call is complete, press the Drop button, but don't hang up the handset. While holding the handset, you can press the Work-Code button and enter the code with no problem.
I would recommend that you make sure the 4620 users use their headsets and that their headset button remains illuminated at all times.