On of the two external monitors flickers on Ubuntu 14.04

I have two Dell E2211 monitors connnected to my Dell latitude E7240 having Ubuntu 14.04 with integrated graphics.
M1 : Connected via VGA to mini DP converter
M2: Connected via DVI to HDMI converter.

When I switch on in the morning both work properly for 2-3 hours. But with time M2 starts flickering and after sometimes go off. And sometimes suddenly starts working.
When M1 is unplugged, M2 works without any problem. What should I do to solve this problem.

xrandr output:

Screen 0: minimum 8 x 8, current 3840 x 1848, maximum 32767 x 32767
eDP1 connected primary 1366x768+1271+1080 (normal left inverted right x axis y axis) 277mm x 156mm
   1366x768 60.0*+ 40.0
   1360x768 59.8 60.0
   1024x768 60.0
   800x600 60.3 56.2
   640x480 59.9
HDMI1 connected 1920x1080+1920+0 (normal left inverted right x axis y axis) 477mm x 268mm
   1920x1080 60.0*+
   1280x1024 75.0 60.0
   1152x864 75.0
   1024x768 75.1 60.0
   800x600 75.0 60.3
   640x480 75.0 60.0
   720x400 70.1
DP1 connected 1920x1080+0+0 (normal left inverted right x axis y axis) 477mm x 268mm
   1920x1080 60.0*+
   1280x1024 75.0 60.0
   1152x864 75.0
   1024x768 75.1 60.0
   800x600 75.0 60.3
   640x480 75.0 60.0
   720x400 70.1
HDMI2 disconnected (normal left inverted right x axis y axis)
VIRTUAL1 disconnected (normal left inverted right x axis y axis)