My iPhone's battery runs down frequently after being fully charged, what can i do?
Based on the "iphone" tag on this question, I'm going to assume you're talking about an iPhone battery. The lithium-ion batteries used in portable devices have a limited "lifespan" (number of charge cycles) -- their maximum charge capacity diminishes slightly every time they are charged.
Unfortunately, iPhone batteries cannot be easily replaced by consumers, but Apple will replace them for $86 with a one-week turnaround. There are also third parties that offer to do this cheaper, but it may affect your warranty if they are not authorized technicians.
Finally, if you are really into DIY, you can buy the parts online and replace it yourself (about $30 including tools and shipping), though some have suggested that this is a difficult procedure.
Poor battery life can be for a variety of reasons these include:
• Location Services in regular use, like Siri geofencing in reminders/passbook or a GPS app using it a lot. Check Settings > Privacy > Location services (in iOS 6) to see what's using it.
• A mail account that's not set up properly or had stopped working correctly from a restored back up, for example the outgoing mail server password not being entered on an IMAP or Exchnage account.
• Push mail being switched on. Settings > Mail > Fetch, to see how it's set up.
• An app that's misbehaving and using a lot of CPU time (you may notice the phone warm up a little). Check your logs in Settings > General > About > Diags and usage > Diags and usage data, for anything unusual. Also check Settings > Usage - Time Since Last Full Charge to see if the time used makes sense, have you been using the phone for as long as it says? If the Standby time and in Use time are the same then something is running in the background.
• Using the phone in a poor reception area will dramatically lower battery life, even in its on standby.
• A corrupt restore from back up.
Things to do to try and resolve the issue:
• Power cycle the phone
• Reset user preferences. Settings > General > Reset > Reset all Settings.
• Restore phone in iTunes and set up as new. (Most invasive option, but will sort the issue).