And a democracy can easily become a dictatorship.
I agree with you in that re-offending prisoners should have their rights to vote revoked as they have continually shown that they do not wish to live by the rules of this society.
In saying that we must be careful with such decisions as they can get out of control very quickly.
Democracy is highly dependent on variety. It is dependent on people having different view points from one another and aligning their viewpoints in a way that will be beneficial for society.
If there were to be a situation in which a large portion of the population starts to think in a certain way which is potentially harmful to society, we may get into a situation where they could vote to change to a dictatorship (extreme example).
Though the likeliness of that ever happening is really really really small. No system is bulletproof.
..so tyranny naturally arises out of democracy, and the most aggravated form of tyranny and slavery out of the most extreme form of liberty? (Plato: The Republic)
Yes and no. As long as we still have people that are different to one another then we're safe. It's only when people become the same, personality copies of each other, do we find ourselves in a bit of a pickle.