It can be stored in a closed container indefinetly. Although not boxing related, I found this fact interesting and wanted to share it. I cook with Balsamic Vinegar quite a bit, it adds a subtle nutty flavor. Below is an interesting story of its origin.
Store the product at 39-86°F, but refrigeration is not required. Exposure to air will not harm the product, but may cause “mothering,” which causes the solids to filter out. Some sedimentation is normal for a product that contains a high level of soluble solids, but the sedimentation will disappear when the bottle is shaken.
Traditional Balsamic Vinegar of Modena (Italy) is made from white and sugary Trebbiano grapes grown on the hills around Modena. Custom demands that the grapes are harvested as late as possible to take advantage of the warmth that nature provides there. This vinegar is made from the cooked “grape must” [the juice pressed from grapes before it has fermented; new wine] matured by a long and slow vinegarization process through natural fermentation, followed by progressive concentration by aging in a series of casks made from different types of wood and without the addition of spices or flavorings. The production of traditional Balsamic Vinegar is labor intensive and time consuming; this accounts for its high cost and limited availability.
Production of traditional Balsamic Vinegar is governed by Italian law and provides that a specific Certification Agency (Cermet) oversees all production phases, from the vineyard to the bottle. All of the product that is bottled must pass a sensory examination run by a panel of five tasting judges.
Commercial grade Balsamic Vinegar of Modena constitutes a more economical alternative to the traditional product. In the United States, products are also allowed to be labeled as Balsamic Vinegar, based on the U.S. labeling laws. These products are made from the juice of grapes, but would not carry the term “of Modena” on the label. Traditional Balsamic Vinegar of Modena generally is found in specialty stores. Commercial grade Balsamic Vinegar of Modena can be found in specialty stores, supermarkets, and supercenters.Commercial products are of high quality and suitable for use in marinades, vinaigrette dressings, and in making pan sauces.

