IMac external display (EA232WMi) won’t sleep

I'm using an iMac 11,3 (27 inch, mid 2010) with an external display (an NEC EA232WMi).

Over the past week or so (beginning just prior to 10.9.2), when the iMac's display sleeps, the external display won't stay asleep.

It keeps waking up.

I can see the power indicator repeatedly going back and forth between the "on" and "energy save" modes. When it wakes, it shows its usual message about not receiving any video input signal. The iMac's internal display doesn't (visibly) do anything at all.

It doesn't seem to be related to any apps– if I reboot the iMac and leave it there at the login screen until the display sleeps, the same thing happens.

This only happens when the display is off but the iMac is still awake. When the iMac sleeps, everything seems normal.

If I move the external display to a different Mac (which is also running 10.9.2), the display sleeps normally, so it seems to be specific to the iMac.

I did an SMC reset and even zapped the PRAM (yes, voodoo) but they had no effect. What can I look at to figure out why the iMac keeps waking the external display?

Additional: Wondering if this might be related to an external device, I tried unplugging everything from USB. No change. Turned off Bluetooth? No change.

Update with some requested information:

1. Console logs. All that I get is the following. In this test, the main display slept at 10:10 AM and the external display problem appeared. I let it continue until 10:16 AM. These are all the messages that appeared in Console.

   3/15/14 10:10:14.227 AM WindowServer[127]: device_generate_desktop_screenshot: authw 0x0(0), shield 0x7fa8028e4910(2001)
   3/15/14 10:10:14.253 AM WindowServer[127]: device_generate_lock_screen_screenshot: authw 0x0(0), shield 0x7fa8028e4910(2001)
   3/15/14 10:10:14.581 AM WindowServer[127]: device_generate_desktop_screenshot: authw 0x0(0), shield 0x7fa8028e4910(2001)
   3/15/14 10:16:10.580 AM WindowServer[127]: handle_will_sleep_auth_and_shield_windows: Deferring.
   3/15/14 10:16:10.582 AM WindowServer[127]: CGXDisplayDidWakeNotification [59971881496111]: posting kCGSDisplayDidWake
   

2. System report "Graphics" data. Looks OK to me, let me know if you see anything that seems wrong.

   ATI Radeon HD 5750:
   
     Chipset Model:    ATI Radeon HD 5750
     Type: GPU
     Bus:  PCIe
     PCIe Lane Width:  x16
     VRAM (Total): 1024 MB
     Vendor:   ATI (0x1002)
     Device ID:    0x68a1
     Revision ID:  0x0000
     ROM Revision: 113-B9710C-238
     EFI Driver Version:   01.00.417
     Displays:
   iMac:
     Display Type: LCD
     Resolution:   2560 x 1440
     Pixel Depth:  32-Bit Color (ARGB8888)
     Main Display: Yes
     Mirror:   Off
     Online:   Yes
     Built-In: Yes
   EA232WMi:
     Resolution:   1920 x 1080 @ 60Hz (1080p)
     Pixel Depth:  32-Bit Color (ARGB8888)
     Display Serial Number:    1X312924NA  
     Mirror:   Off
     Online:   Yes
     Rotation: Supported
     Connection Type:  DisplayPort
     Television:   Yes
   

Update 2

In case it helps, I uploaded a system profile of my iMac which I generated using system_profiler -detailLevel mini.

Update 3

Since @Buscar웃 is deleting their answer, I'll add these details here:

• "Wake on Network" is disabled
• There's no screen lock (no password required to wake the Mac)
• All sharing services have been disabled (several were active, including screen sharing and DVD sharing, bu disabling them had no effect).

Update 4

In case it's useful, the cycle time of the wake/sleep process is 8 seconds. Meaning, if I watch the display and its power indicator, this cycle repeats every 8 seconds:

• Monitor shows its "no signal" screen
• Monitor goes into power save mode
• Monitor comes out of power save
• Repeat

Update 5

I tried doing a safe boot; this also had no effect.

Update 6

Just for completeness I also used the external display's menu system to reset it to its factory defaults, but again, this had no effect.