MBP falling asleep external monitor circular on-off

I have a very particular issue, for which I was unable to find answer on the whole Internet.

1. I was using a minidisplayport to VGA adapter (original Apple) to connect to the external monitor. When I put the computer to sleep, the the MBP (early 2011) goes to sleep, the external monitor goes to standby. This is the normal operation.
2. I recently upgraded to a larger external screen, which has VGA, DVI, and HDMI input. Obviously I tried a minidisplayport to HDMI cable. When I turn the MBP to sleep, it takes some time to finalize the process, I suppose due to the 16GB RAM. However, during this time, i.e. between the moment I click the sleep button and the MBP actually falls asleep, the external monitor (connected via minidisplayport to HDMI cable) turns off, and then immediately turns on. Turns off, and then turns on. Off, and again on. This process cycles until the MBP finalizes the sleeping process.

I would not like to go back to the minidisplayport to VGA adapter. Love digital, but this is not the correct behaviour.

This behaviour is acutally super-annoying, not to mention its effect on the monitor electronics. I wonder if anybody has a guess what can be done to prevent this.

Many thanks for any help in this regard in advance!