Is the battery life noticeably shorter? If so it may be time for a battery replacement.
If it hasn't been done, one thing to try is let the phone sit on the charger for at least an hour after it's fully charged. Do not plug it in to charge again until it is at the point where it shuts down for a low charge. Again charge it at least for an hour past where it's at 100%.
Note that the extra hour+ past 100% is because some devices aren't quite at 100% when they indicate that they're fully charged. This may not apply to the iPhone in question, but it can't hurt when leaving it plugged in overnight is easy enough to do.