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.

The lower temperatures cooking sous vide helps with retaining moisture in meat. While the myosin contracts in the 104-122 F temperature range, actin denatures at a much higher range of 150-163 F. Braising takes the meat up past the actin temperatures, but with sous vide you can keep it below.
(Note some online sous vide recipes say to use a higher temperature, so look for ones that keep the temperature below 150.)

A good explanation with pictures is here: Heat and Its Effects on Muscle Fibers in Meat

This problem cannot be solved, not with sous vide and not with something else.

Meat is made of cells, whose walls are made mostly of proteins. These proteins change their structure when heated, and that's what turns raw meat into cooked meat. When they change their structure (denature), you get tears in the cell walls.

When you have a piece of meat which is poor in collagen, say a steak, you only heat it enough to denature only the myosin, and most other proteins stay intact. Some of the juices flow out, but most of them can be held back by the still existing cell walls.

If you were to do that to meat rich in collagen, you would end up with impossibly tough meat. So you expose that to enough heat for long enough time that all the tough collagen changes thoroughly and turns to smooth, lubricating gelatin. Braising is one of the methods to do that. When this has happened, all the other proteins are far, far gone, and all the liquid from the cells has flowed out through the now-shredded cell membranes. If you are braising, it flows into the braising liquid, if you are doing sous vide, you will find it in the pouch. This type of cooking is incompatible with the juices staying in.

If you are missing flavor in braised meat, you might be braising the wrong type of meat. Some milder flavored meats like chicken and animals raised on mass production farms (little movement, no variation in food, no fat, slaughtered young) are simply not gamey enough. If you braise mutton, or a hog, or wild fowl, with some fat marbling too, you will certainly have flavor in the meat itself. Not because of juices, but because the meat is aromatic. Even worse, if you are braising meat parts from mild tasting animals which are low in collagen, you will not only lose the juices, you won't have the gelatin either, and you will end up with dried lumps of tough, tasteless matter.