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Make sure you cool it properly (by placing the pot of stock in ice water) before refrigerating.
And I would also bring ti to a full boil before use, especially if its been in the frigde for a couple of days.
Stock also well in the freezer -- just make sure it is well-sealed, because it too can get freezer burn. If it's protected from air, it can keep for months in the freezer.
General rule is 4 days maximum in a good refrigerator and sealed container. This depends on the quality of the stock, whether or not it was cooked and cooled properly, and provided that people respect the stock while it is in storage. If a stock is not brought up to and then held at temp throughout the cooking process, and/or if poor ingredients are used, it will not last long (as well as simply be a bad stock from the get-go). The faster the better for cooling. If not cooled properly, a stock can spoil in as little as 5 or 6 hours. So 4 days max for a good stock, certainly less if something wasn't done right. Bearing all that in mind, always taste your stock before using it. If it tastes off (for whatever reason), your dish will be off, and the stock is useless. If your daily production does not allow for frequent stock making, freezing is a good option, but that too will reduce the time it can be held in a refrigerator once thawed.
A parchment lid will keep airborne particles out of your stock while allowing steam to escape, so water won't drip down the inside of the pot as much, dragging scum with it. As the liquid reduces, the lid will move and keep a closer contact. It takes a bit more maintenance than a solid lid, but if managed well, it provides a better end product.