<p>Occasionally, while printing, my <em>y</em> axis will slip and the layer will, from that point forward, be shifted, ruining the print.</p>

<p>What might be the causes of an axis slipping? I have tried cooling the motor which seemed to have been getting warm, and the belts are not too tight.</p>

<p>This does not happen with every print, and seems to be an intermittent problem. </p>

<p>My printer is a MendelMax RepRap, and the <em>y</em> axis is my moving bed.</p>

From what I've experienced, there could be three potential reasons.
Your belt(s) could be loose. Simply loosen your Y-Axis motor and pull the motor until the belt is slightly more than taught (it will relax into a taught position). Then, tighten the motor securely in its place.
One of your axis endstops could be triggered mid-print. If you have a larger print, you run the risk of hitting an endstop, which could cause the machine to lose its coordinate system.
I found on my machine, if you run your program via USB (on MakerWare specifically, possibly others) there might be some sort of lag in the serial connection that could cause the entire program or coordinate system to shift. I repeated this issue multiple time using a USB connection and fixed it (repeatedly) by either running off of an SD card, using a different slicer (in my case the Cura plugin for OctoPi), or trying an earlier version of your software (this was my long term solution).
The latter worked best for me. I tried running MakerBot Desktop on my Dual Replicator 1, but ran into the same exact issue as you. In fact, I encountered this issue around firmware 5.0 on the Replicator as well (7.? is the latest). Finally I switched back to using MakerWare 2.4.? and everything worked fine.