Suggest a reason why proteins may precipitate at certain pH's but soluble at other pH's?

Many of the amino acids have side chains that can exist in two different protonation states (take glutamic or aspartic acid for instance - it can be COO- or COOH). In a folded protein, the state of the individual side chains can be very important, because it is interactions that hold the protein in its native state. So say that your glutamic acid participates in an electrostatic interaction via it's COO- to a positively charged side chain. If you change the pH you may convert that to COOH, it loses the interaction, and your protein is on the road to unfolding (precipitating). Also, charged residues on the surface are important for solvating the protein in water. If the surface of the protein is neutral, it is unhappy in water, same result. This is why it's not a good idea to take your protein of interest through the pH that is its pKa (the pH where it has an overall neutral charge) - it will often precipitate out on you.