There are some apartments that will do 3 months, but be prepared to pay a sweet price. You have to remember they have to pay to get ready for you and for the new tenants and everything is expensive. I can help you find a 3 month lease if you are willing to pay a good price, but it is in the Alamo Heights area where the sweet prices are common. Call me or email me if you need assistance.
Generally it is difficult to lease for this time period but in most cases, it is clearly up to the owners if the property is being managed. Hope this helps. If you have further questions, feel free to call me.