can the iPad2 run on charger 24-7

I have a iPad2 running 24-7 displaying via the MD098ZM/A HDMI adapter to a large LCD screen. The iPad is charging all the time with the supplied charger plugged into the 30 pin connector coming off the video adapter. The iPad starts at 100% then seems to discharge but then come back up. Never runs at 100% power. Is the charger strong enough to run the iPad 2 in a 24-7 environment?

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