iPhone brightness keeps dropping

Have you tried to reset your phone, to see if a reset resolves the issue.

Try this:

Go into a dimly lit or dark room.
Open your Settings app from the Home screen of your iPhone, iPad.

Tap on Brightness & Wallpaper.

Turn the auto-brightness setting to Off.

Adjust the brightness slider to the level you would like your screen brightness to be at in the given area. if you're in a completely dark room, you'll probably want to put the slider all the way to low or pretty close to all the way down.

Turn the auto-brightness setting to On again.

Turn on your light switch.
Watch the brightness slider move upwards to adjust to the new light entering the sensor.
As long as the brightness slider is moving on its own, you have just re-calibrated the sensor and it should work properly from here on out.

Try this and it should work....Good luck.

Is your phone in a hot environment (in direct sunlight, tethering long periods making the phone hot, etc.) when this happens?

If the phone becomes hot, the screen will not go to "full" brightness until it cools down. It also may automatically slow its charge rate or refuse to charge at all and if even hotter, may disable completely and show a "warning- too hot" type of message on the screen.

Keep in mind, these are basically very powerful very tiny computers and have no fans and no real heat sink with fins to keep themselves cool.

My Android tablet has done this from new, and my iPhone 4 did it. The i5 has been ok when it comes to the screen auto brightness.

Like another poster suggested, it sounds like your phone is trying to protect itself from overheating and reducing the brightness when out doors.