Your Latitude's power management software can probably "tell" that there is insufficient power to power the machine and charge the battery simultaneously - this might explain the spontaneous shutdown.

Another test you can do is to try to charge the battery when the laptop is powered off (such as during meal time). Often with machines that draw ~90 watts, you can do one but not both simultaneously.

When I was shopping for my current laptop, I avoided anjy machine whose specifications stated a power draw greater than 75w. Many Lenovo and Fujitsu model adhere to this standard.