Firstly, a beautiful piece.
Secondly, that first rhyme sequence really doesn't work well and it ruins the deep feeling of the piece that I know you have intended to evoke.

Therefore perhaps try changing:
'faded up' to 'faded so'
'fell in the cup' to 'it could not grow'
'as a pup' to 'in such woe'

SO IT WILL BE:
My white rose started to wither, its fragrance faded so
My white rose could not survive the drought, thus it could not grow
My white rose never got back
My white rose petals got black
My white rose took the memories, leaving me in such woe

The first two rhymes of the '-up' style worked but the last one seemed very forced. I think my suggestions would also help with the emotional impact that the piece would have overall.

Ignore me if you choose. (:

5/5