Symptoms

Whenever the user would attempt to edit/set the data source for a drop down list and/or choice control the Designer would just spin as though it were loading something despite loading nothing no matter how patiently we'd wait.
 

Diagnoses

Given that the issue seems to have appeared out of the blue we can't really say what specifically happened to cause this but the HostServer logs revealed this error:

Event message: An error occurred processing a web or script resource request. The requested resource 'pSourceCode.Forms.Controls.Web.ControlPack|SourceCode.Forms.Controls.Web.DropDown.PropertyConfiguration.JS.PropertyConfig.js' does not exist or there was a problem loading it.

That seems to indicate an issue with the SmartForms control pack
 

Resolution

Running a repair of the Control Pack on the K2 box resolved this error.