Alberto came over to have a look at the laser and discovered that the diode temperature was continuously increasing the longer the laser was kept on. The crystal temperature remained constant. He turned off the laser and shut the shutter, jiggled the cable connected to the laser a bit, and turned it back on. Lo! The temperature no longer increased...

So for the time being the laser seems to be fixed. If these problems start happening again, however, I may have to do some more rigorous troubleshooting/actually find out what's causing the problem.