I know you said you were sitting there, but as for anyone else, like all other farming methods, you have to stay in the same chunk (or range of chunks) as the farm or else the chunk will not load and the farm will not grow. This goes for being too far away from your farm within the nether or being outside of the nether
This video explains just about everything you'll need to know about Nether Wart.
I watched the video, and while it is very good (as is the Part 1 video), I believe he is incorrect in saying that planting in multiple chunks increases the average rate at which the netherwart will grow. If chunk updates occur as he stated, then there's a logic error in his probability.
He said the game picks 20 blocks from each chunk and checks them for updates. Assuming that it can pick ANY block, and not limit itself to ones that can update, then each block in that chunk has an equal chance to be picked.
So if you have four 8x8 plots of netherwart, it doesn't matter if all four plots are in the same chunk, or if they are in four separate chunks. The odds of each block updating are exactly the same.