You are fortunate to have a tree poinsettia in your back yard. Don’t overwater it. Poinsettias growing in the ground are drought resistant once established and need no special care. Droopy leaves can be caused by too much water, not only by too little. Also, they often drop lower leaves and in some climates are deciduous. This summer has been unusually hot and this too could have caused the leaves to droop.

You do not tell me what climate zone you live in. Neither do you mention the type of soil you have. Also I can’t quite understand from your description what you mean about “setting up a gallon water bottle and the plant seems to drink.” Does this mean it’s in a container? If so, you are killing it by overwatering. Mighty few container plants can stand being watered every day. As a general rule watering any plant every day will eventually lead to root rot. I the plant is growing in the ground, try getting on the edge of the roots and digging down (making sure not to damage roots) and see how wet the soil is. Don’t water until the top six or eight inches are dry and then water deeply and wait at least a week before watering again. If drainage is bad and you have clay soil, apply gypsum according to package directions and irrigate into the ground with next watering. If the plant is in a container, dig down with your hand and feel the soil. Do not water again until the top two or three inches of soil are dry. Make sure water pours out the bottom when you water. If not, the hole in the bottom of the pot may be clogged with roots.

 Poinsettias need well-drained soil, full sun, and cutting back in spring.  You can make new plants simply by sticking the cuttings into the ground. (My organic book has instructions. If you don’t have a copy, see if you can find one in your local library. Or you can purchase the Kindle edition quite cheaply.) I also suggest you see what it says about poinsettia (Euphorbia pulcherrima), in Sunset Western Garden Book.