There are several reasons why this might happen.
- Bad batteries. Compact cameras have considerable power drain. When using non-rechargeable batteries, use premium quality alkaline cells only. Cheap carbon-zinc cells won't work well. Also, beware of counterfeit "premium" batteries. If you're using rechargeable (NiMH) cells, the cells may have degraded - this may happen for several reasons. Standard NiHM cells have considerable self-discharge, leave them on the shelf for a few months after charge and they may lose more than half of their charge. They may also become "lazy" after lying around unused for long periods. NiMH cells can be a godsend - I have not used a single disposable AA cell for nearly a decade - but they do need a bit of attention.
- Dirty or corroded contacts. The contacts in the battery compartment may become dirty over time, or a set of batteries left in the camera may have leaked and corroded the contacts. If they're only a bit dirty, a pencil eraser can be used to clean them. If they're corroded (with green crud on them) a good wipedown with fine emery paper might be a more appropriate solution. The contacts on the inside of the battery cover are easy to clean, cleaning those on the bottom of the battery compartment requires a bit of patience.
- Faulty electronics. Sometimes, electronic equipment may develop faults that result in excessive power drain, which means batteries run low very quickly. In this case, there's not much you can do: diagnosing this sort of problems requires extensive troubleshooting skills and at least a decent multimeter.