I am sorry to hear that you have been experiencing weakness in your knee that is limiting your ability to run. I cannot comment specifically on your case without doing a thorough evaluation. However, below I will provide some general information that you may find helpful.
A feeling of weakness or fatigue in the knee while running can come from a variety of sources. This symptom can be from weakness in specific knee or hip and glute muscles, or can be influenced by the low back or ankle joints.
An ankle sprain, even once it is past the phase of being painful, can be accompanied by residual weakness, stiffness, or excessive movement that can result in running gait changes that influence both the injured leg as well as the opposite leg. For these reasons, it’s important to have a thorough assessment by a physical therapist to determine what is contributing to your knee weakness.
Additionally, the rate of training progression can influence how the body and joints respond as your mileage increases. The general rule with building up your mileage to prepare for a longer race like the half marathon is not to increase weekly mileage by more than 10 percent per week. This will allow your tissues adequate time to adapt to the increasing load of running for longer.
Physical therapy could be helpful in this situation, as a physical therapist would be able to perform a thorough evaluation of your knee, and your opposite ankle. They would be able to determine if other joints are contributing to your symptoms and if any muscle weakness exists that may be contributing as well. They will also be able to analyze the way you run, to ensure that you are running in a way that is the most safe and efficient for your body.
A physical therapist would work with you to develop a plan to work toward your goal that may involve a combination of useful information, manual treatment, and targeted exercises.