Well, obviously you have a protein that is very resistant against chemical denaturation. This is something relatively common. Proteins are usually made in nature for a certain purpose. This means that they have to be stable enough to perform their function but not too stable as this may affect flexibility and/or degradation of the protein. However, life has also evolved in extreme (cold, hot, salty or even acidic) environments and organisms that can survive extreme conditions usually have proteins that are able to function under such circumstances. As an example for a very stable protein fold I recommend the following paper as a start: http://www.ncbi.nlm.nih.gov/pubmed/17557327

I hope this helps a bit. Cheers.

Carbonic Anhydrase has been reported to be quite stable over a wide range of pH: between pH 4.0 and pH 11.0 - although not as low as pH 2.0. Its thermal stability and folding has been studied in some detail by a Swedish group.

Martin Karlsson, Lars-Göran Mårtensson, Bengt-Harald Jonsson, and Uno Carlsson.

You may want to read some of their publications.

The problem is to understand why your protein is stable with pH. Typically in globular proteins the protonable side chains induce conformational changes .varying the pH. An analysis of the sequence and its physico-chemical properties should facilitate the analysis. Another consideration is to assess the location of these residues in the three-dimensional structure (internal or external). An activity assay at different pH (where possible) may help to recognize their contribution. Another option is that we are dealing with an IDP but it is less probable because these proteins show high net charge and are often strongly pH dependent. However, because they experience an ensemble of conformations in solution, what you see by SEC is the average distribution of gyration radii that might be the same even if the internal weight of conformations is quite changed by pH.