Instructions
Verify that the peripheral is receiving power. If it's a rechargeable, fully charge the device before using it. If it uses batteries, try adding new batteries even if you know the current ones aren't dead.
Move closer to the PS3. Ideally, you want to be within 15 feet of the console. Disconnect any other wireless devices (such as other Bluetooth peripherals) that are nearby and make sure the PS3 is visible and not blocked by any walls or shielding if it's being housed in an entertainment center.
Re-pair the Bluetooth device with the PS3. Hold the "Sync" or "PS" button on the Bluetooth device and select "Add New Device" from the "PS3 Settings" menu. If this does not work and if you have the option, try pairing the Bluetooth device to a different PS3. If it works then, the syncing mechanism on your PS3 may be malfunctioning.