My Lenovo laptop shuts down with no warning after about 45 minutes of usage when not plugged in?

I have a Lenovo T430s ThinkPad and lately it has been shutting down very quickly without warning when I have it on battery. I don't think it's the battery, because I don't get any warnings or anything about battery life and the laptop will still have like 3 or 4 hours of battery life left on it when it shuts down. I think I can trace the first episode of this to around the time I had just started using Skype on my laptop. Is it maybe the fan allowing it to overheat? I use the laptop on a hard surface even when it isn't plugged in.