There are a number of possible explanations for the problems you're having.
You are growing the plant hydroponically. Hydroponic plant roots need oxygen from moving water, or a large enough water surface to replenish oxygen. If they don't, they can rot. I suggest removing the plant from the water and smell it to see if the roots are rotting.
The plant should also have regular water changes using distilled, spring, or rain water. Both chlorine and fluoride in tap water can damage the plant. You can vent chlorine by letting water stand for 24 hours but you can't remove chloramines or fluoride this way. You also need to fertilize the plant once in a while. You can either use a specialty lucky bamboo fertilizer ( a few drops ), or some aquarium water which is what I do.
Letting the roots dry out as you said happened once, can damage the plant. Did this damage start shortly after that incident.
And the plant likes diffuse lighting and not direct lighting. I note that you have it near a window, and it may be getting too much light which can turn the leaves yellow, and I see your plants leaves are yellow.
I'd be inclined to prune the plant below the brown area, and seal the cut with candle wax. Change the water with bottled water or rain water once a month until it recovers, and move it from the window.