For anyone still having problems with the Intel graphics driver not loading either randomly or consistently (especially consistently) would you mind trying a small experiment? It sounds rather unrelated but surprisingly enough it seems to be working for me. It involves replacing MDM with GDM and then testing by simply using your computer for a few days and running "inxi -Gx" to check which driver is loaded after every boot/reboot. This is very simple to do and is easily reverted back to MDM.
Open Synaptic, search for and install "GDM". When you hit "Apply" you will see that MDM (only) will be removed (leaving all your themes and settings intact, by the way). Next, during installation, a box will appear asking you to choose between MDM or GDM as your display manager. Choose GDM from the drop down menu. Once installation is complete, simply reboot and you're done. Login as usual after reboot, open a terminal and run "inxi -Gx" without the quotes and see if the correct Intel driver is loaded, not the "Gallium .04 on llvmpipe" software driver.
If the correct Intel driver is loaded then just use your PC/laptop normally for the next few days (if you wish, reboot several times just as a primary test). The point is to see if the correct Intel driver loads every time without fail over a period of several boots/reboots (after a power-down and cold boot as well). If it does, then revert back to MDM (same procedure as above except that you're obviously installing MDM vs GDM--just as simple) and run MDM again and test the same way just to see if it fails to load the Intel driver over a period of several boots/reboots.
I've been running GDM in place of MDM for a day now without a hitch--the correct Intel driver has loaded every time so far but that doesn't mean much...yet. I thought that using the "xorg-edgers" ppa helped some but last night the gallium driver was loading every time, all the time and the same thing this morning. Switching to GDM solved seems to have solved that problem so far. Whether it's a problem with MDM or MDM just needs to be reconfigured I haven't figured out yet.
Please let me know how this works for you?
"Humph. Choice, it is the quintessential Linux delusion, simultaneously the source of it's greatest strength, and it's greatest weakness." (All apologies to The Architect)