If I have a desk job and have been out of work for 4 months because of a sore knee, can I get fired?

Yes, you can be:
1) Employers are not required to allow employees to miss work unless a) the employees have and use paid time off (PTO), like sick days, to cover all the absences; and/or the employees are eligible for, the company is covered by, and the employee uses FMLA leave for a medical absence. However, even if your company is covered (50 or more employees) and you are eligible (worked there at least a year), FMLA leave is only 12 weeks/3 months; therefore, you have exceeded, based on what you write, your maximum leave. Once you can no longer cover an absence, even for medical reasons, with PTO or FMLA leave, you may be terminated; the law does not require employers to keep employees who cannot or will not come to work.
2) You say you have a "desk job"--there is no reason you have to be out of work for 4 months from a desk job for a "sore knee" in order to have therapy 3 times per week. (I am also speaking from personal experience of having had a desk job and having had, simultanously, severe chondromalacia  in my knee and very bad lateral epicondilytis in an elbow and requiring multiple therapy sessions per week--I missed only the actual hours required for therapy, and so was at work the vast majority of each week.) While the law requires "reasonable accommodations" for employees with disabilities, it is not reasonable for a desk employee with a sore knee to be allowed to miss 4 months of work.
If you miss as much work as you describe missing for the stated reason, the employer may terminate you.