Vostro 3560 loosing connection to HDMI after 20 minutes

I'm struggling to connect my Vostro 3560 notebook to a projector. I've managed to make it work after reinstalling the video drivers, but the connection lasted only for 20 minutes and went black suddenly. Since then I see "no signal" on the beamer and cannot make it work again.

I'm using official video drivers from following Dell's website:

http://www.dell.com/support/home/us/en/19/product-support/product/vostro-3560/drivers/advanced

I updated the BIOS.

The projector is fine, worked yesterday for several hours on VGA.

The cable is fine, worked on my wife's Dell notebook for at least 1 hour.

My power options are probably fine, because everything is set to "highest performance".

I'm suspecting the problem in over-heating of the notebook, but even after a longer break, when notebook gets all cooled down, it still won't connect.