Troubleshooting process: Pi stops the script, doesn’t reset

Twice within the past 48 hours, my GroveWeatherPi’s script has quit running. I first notice this via notification from WUnderground. Last night I was able to SSH into the RPi just fine after the WUnderground notification. I checked the OLED and it just stopped, though the RPi was still running. I rebooted the Weather Station to try to get it to go again, but there wasn’t any love from that. So, then I did a hard reset and was able to start it up again. It ran about 12 hours, then did the whole thing all over again, RPi still running and I’m still able to SSH in, and do a hard reboot, then start the script again.

My questions are: 

• Will the log help me locate the problem? Where is the log located? What should I be looking for?
• Overall, are there any boards or other troubleshooting approaches I should look at first? The station’s been running faithfully about five months now.