Were there any hardware or system changes / updates around when this first started, particularly graphics drivers, etc?
Are you playing on PC or Mac?
A handful of people have reported this with D:OS EE, more commonly in OSX (some issues more severe that others; one had no problem with clicking through for movement, for example, just when the cursor was over something that could be interacted with, and a couple it was only certain parts of the UI that they could click through).
Does this happen now regardless of the display mode? Does it happen in windowed mode?