MacBook Pro Retina 15" (Early 2013) randomly shuts down
I realize it's been a long time since the initial post and unfortunately I don't have a solution, but I'm going through what appears to be the same problem and, as there seems to be scant documentation,  I thought I'd report a couple more details to see if they jog any ideas in anyone and if they line up with your original report. On running syslog | grep shutdown I get the same response: 

localhost com.apple.xpc.launchd[1] (org.cups.cupsd) &lt;Warning&gt;: Service has increased maximum shutdown time to 60 seconds. This will create a poor experience for the user.


On contacting support, Apple is also presuming this to be a battery issue, but they (or anyone else for that matter) can't explain how/why the spontaneous shutdowns would occur when on AC power. 

So, a couple things I've noticed:


Running yes &gt; /dev/null &amp; in terminal prevents the random
shutdowns. I've seen this workaround in a couple places but not
connected to the 'maximum shutdown time' we're both getting
While running gfxCardStatus to lock the graphics card to either
integrated or the discrete nVidia card, I get different shutdowns.


On integrated graphics:
 - I get a black screen, but with the LED
       panel clearly still on and the keyboard backlight stays on (if it
       was on before). The fan runs loudly and the black screen remains for
       about 10 seconds, then the computer shuts down.
 - to my best recollection, this only happens on battery power.

On discrete cards:
 - rather than going black, the screen freezes. The rest is the same
    (fans, shutdown after about 10 seconds)
 - happens on both ac and battery power

Anyways, hopefully that spurs some idea in someone. Seems like everywhere I look or anyone I talk to has different advice on cause and solution, but your original question is the only one I've seen that's exactly the same as what I'm going through (with the minor exception that my laptop is a late 2013 15" model).