It all depends on the half-life of the particular isotope which is causing the radioactivity. (Half life is the length of time it takes for the substance to lose half of it's radioactivity) For example, something like Sodium 24 has a half life of 15 hours, but uranium 238 has a half life of around 4,500,000,000 years. Some of the man made elements have half lives measured in fractions of a second!
I'm pretty sure the size isn't a significant factor. I recall that the radioactivity never actually reaches zero. Is that right? If that's the case I suppose there comes a point where it's considered to be negligible..
Firstly it depends on the element in the rock that is decaying some take longer than others to decay.
It depends on how much of that radioactive material is present to start with
It depends on when you decide to say something is not radioactive. ( Whether you mean below what is dangerous to a person or whether you mean to below background level )
On a practical level you can never get to zero as there's always a possibility of a decay later on.
Perhaps if you can give us some more background information we can give you a better answer.