macbook pro (mid 2009) randomly shuts down

My wife's Macbook Pro started to randomly shut down a couple months ago. She has been horrible about upkeep and has been fairly hard on the computer in general, but it has been great for her until this. Other than the random shut downs it had also become very slow, it only had a 150 GB hard drive that was maxed out, 4 GB RAM, would only hold a charge for about 1.5 hours and was still running Lion. So I thought to fix everything I'd install a new SSD, get the RAM up to 8 GB, and replace the battery. Now it starts up in 6 seconds, holds a charge for many hours, runs Yosemite, and has 235 GB left on its SSD. But it keeps shutting down randomly. This makes me think there is a problem with another piece of hardware since I did a clean install of Yosemite and only brought over her files on an external hard drive. Sooo... what do you think?