My Motorola Defy will not hold a charge. Had full charge at 8:00 Am and by 2:00 PM battery was dead. No apps running or Wi-FI on. Second day in row this has happened

The DEFY is feature-rich and can run a virtually limitless number of applications, making it useful for many tasks. Your particular usage will affect how long you can go before recharging your battery. Playing games, running applications, and surfing the Web increase the power use of the computer-like functions of the DEFY Calling and texting utilize its phone functions. Depending on your use mix, time between charges will vary. We know you want to use the device to its fullest and offer you these tips to help you get the most from your phone while going as long as possible between charges.
Things you should know about charging your battery.

New batteries are not fully charged. Plug the battery charger into your phone and an electrical outlet. Your phone might take several seconds to start charging the battery.

Tip: It may take several charging cycles for your battery to reach optimum performance.

The battery charger shipped with this device is designed specifically for Motorola mobile phones. Other chargers might take longer to charge your battery, or cause your calls to fail during charging.
Tips to extend battery life:

• During initial set up of your MOTOBLUR account, your phone's battery may drain faster than usual due to the amount of data transferred. After the initial sync, and a few charging cycles, your battery will reach its maximum capacity.
• We strongly recommend to keep the phone attached to the charger during the MOTOBLUR initial sync.
• When not transmitting a lot of data or surfing the Web, set your device to connect to 2G network.
• When setting the phone down after use, quickly press the power key to invoke a blank screen. Selecting a shorter back light duration will also help conserve power by blanking the screen when not in use.
• Lower the display brightness.
• Use the AC adapter to charge your phone whenever possible.
• Toggle Bluetooth, Wi-Fi, and GPS on or off as needed. There are some apps that can help do this easily. While we do not endorse or guarantee these solutions, or provide support for them, some owners have reported success using an application called "Battery Widget " which can be downloaded from Android market.
• Ensure applications are closed when not in use.
• Clear all notifications from the notification bar as much as possible. Click Here to learn more about notifications.
• We suggest charging each night so you start the day fully charged and ready to go!

Motorola DEFY Battery Manager - Benefits

A feature called Battery Manager is now part of the DEFY software

• It provides options for significant battery savings by reducing data traffic when not needed, and by dimming screen when battery is low.
• Two optional settings:

Data Timeout

· With this feature: After a period of inactivity, background data updates stop until the user starts using the device again.

· Without this feature: background data is constantly updated (Email, Social Networking, News Feeds, etc.), even overnight.

Auto Brightness

· When Battery Level gets low, screen automatically dims.

Battery Manager: How To Use It

To access battery manager

1. From the home screen press the menu key
2. Tap settings
3. Tap battery manager

Three Modes are available:

1. Performance Mode (default) - Data Timeout and Auto Brightness are OFF
   
2. Smart Mode - Data Timeout and Auto Brightness are ON with different settings during Peak and Off-Peak times of day. User can change various settings.
   
   
3. Battery Saver Mode - Data Timeout and Auto Brightness are ON with settings to maximize battery savings. User cannot change the setting

I suggest you to give a try on extended battery for motorola defy which is designed by 3rd party factory. It doubled the capacity of the original battery but in return, you need to use a little bulky battery back cover. But it is still acceptable (at least looks ok for me), take a look here:
http://www.batterybay.net/Battery-for-Motorola-MB525-p/motorola%20-cs-mob525xl.htm
You can also find on ebay which is a little cheaper. But ebay seller will not care buyers's issue if the battery is having any problem.