Has anyone solved this problem with braising (other than by sous vide)?
Hervé This has an interesting discussion on this problem in this book.

The process of losing juice when cooking a piece of meat is in big part mechanical. Meat is basically composed of muscle cells tied together by collagen, which is sensitive to heat. Quoting Hervé: 


  When a temperature of 50°c (122°f) is reached in the outside layer, the collagen contracts, compressing the juices inside (although the degree of compressibility is small because the juices are mainly water) and expelling the juices of the periphery outward. The center of the roast, composed of liquids and largely incompressible solids, cannot receive these juices. Anyone who is not convinced of this has only to roast a few pieces of beef, weigh them, and determine their density before and after cooking.


Since heat is transferred from the outside towards the inside by convection, the core of the piece of meat is usually at lower temperatures and retain most of the juices which were not expelled by the contracting collagen in the outer layers. Thus the importance of resting the meat after cooking. Outside the heat, you lose this compressing force and the liquids concentrated at the core diffuse towards the outside and redistribute, giving an improved feeling of juiciness. Following your question, Hervé suggests:


  Given that the juiciness of the meat depends on the amount of juice it has, why not use a syringe to reinject the juices that have drained out from the roast during cooking? 


From this simplified physical picture, I suppose cooking-sous vide for long temperatures and below 50 degrees (temperature at which the collagen contracts) will avoid this phenomenon of expelling juices.