This is probably it. There is no way to tell the remaining charge of a lithium battery other than estimating it from the voltage which drops with the level of charge. It also drops more when it provides more power and this gets worse as the battery is aging (increasing internal resistance). This is why your phone might think that it has 20% battery remaining according to the voltage, but the second you open a power hungry app, the voltage drops below a safe level and the phone shuts down.