Well, let me ask the following.
Are you using a pre-fert. soil like miracle grow or anything?
Are you using your own organic mix? If so what is it?
How far into growth are you?
All this will factor into the answer you need.
but to answer a vague question with a vague answer, Yes, sooner or later the plant will deplete the nutrients in the soil and start to starve to death.
edit: beat me to the draw Haze.