Whether you should leave your backyard umbrella outside during summer depends on what material it is made from. One one end of the spectrum, the more expensive umbrellas that are made from quality Sunbrella material  will withstand the test of time.
Sunbrella performance fabrics are made of 100 percent acrylic and have UV pigments spun into the yarn so the sun doesn't damage the material. You're also looking for a good quality metal pole to make sure it's sturdy.
Aluminum is a good material to keep your eyes peeled for. Meanwhile, if you settle for a cheaper option with a wooden pole and polyester fabric, you may want to fold your umbrella away and store it when not in use so you get more use out of it in the long term.
Whether or not you should leave your patio umbrella open is another question entirely. Closing your patio umbrella after use at the end of an evening entertaining al fresco is a good habit to get into. Practising this will help it stay in better shape for longer and makes it less likely to fall over in the wind.