Hello Megan. This is a very common issue when people first start making stews, so do not feel discouraged at all. The secret to melt-in-your-mouth beef comes down to choosing the right cut and giving the meat enough time at a gentle temperature to break down properly.
First, regarding the cut of beef, you want to avoid lean cuts such as round, sirloin, or generic packages labeled simply as stew meat, which often contain lean trimmings. These cuts lack connective tissue and will turn dry and stringy when cooked for a long time. The absolute best and most reliable cut for stewing is beef chuck roast, also sold as chuck shoulder or chuck eye. Brisket, bone-in short ribs, and beef shank are also wonderful choices. These cuts contain high amounts of collagen and intramuscular fat.
Second, the cooking process requires low heat and patience. Collagen is tough initially, but when cooked gently between 160 and 190 degrees Fahrenheit, it slowly melts into rich gelatin over the course of two to three hours. If your stew is boiling rapidly, the muscle fibers tighten up and squeeze out moisture before the collagen has a chance to dissolve. Keep your stove burner on the lowest setting to maintain a very gentle simmer with just occasional bubbles, or transfer your covered pot to an oven preheated to 300 degrees Fahrenheit (150 degrees Celsius) for even heat distribution.
Lastly, when browning your beef at the start, work in small batches in a hot pan so the meat sears rather than steams. Once browned, deglaze the bottom of the pot with your broth or wine to capture all that caramelized flavor, cover tightly with a lid, and let it braise for roughly 2.5 to 3 hours. You will know it is done when a fork slides into the meat with virtually no resistance.