The literal answer to your question is, yes, an employer can fire you while you are on long term (or short term, for that matter) disability.
While an employee cannot be fired BECAUSE they are disabled, an employer has a business to run. An employee who is unable to return to work after the maximum amount of time mandated by state or Federal law or is unable to perform the essential functions of the position can legally terminated, regardless of whether they are still on disability leave or not.
While I could be mistaken about this, I believe that the only state-mandated medical leave is for pregnancy. Therefore, you would be subject only to the Federal law, which grants you a total of 12 weeks protected medical leave under the FMLA. Once you have taken, either in a block or in intermittant segments, a total of 12 weeks medical leave, the employer has no legal obligation to hold your job any longer, regardless of your medical status and regardless of how legitimate the need for additional leave may be. Your employer would be within his rights to count that portion of the day that you do not work, as FMLA time, and term you when your FMLA time is exhausted.
However, there is one option you might want to consider. Whether it will protect your job or not is subject to factors we do not have available to us; I do NOT guarantee that this will work.
The Americans with Disabilities Act provides that an employer must provide a REASONABLE accomodation when a qualifying employee requests one AND that accomodation would allow the employee to perform the essential functions of your position. IF AND ONLY IF you would be able to perform ALL of the essential functions of your job UP TO STANDARD while working part time, then it MAY be that your employer would be amenable to considering a shortened schedule as a reasonable accomodation. Very, very important caveat: The employer is NOT required to eliminate any of the essential functions of your position from your job description (although eliminated non-essential functions can be considered a reasonable accomodation). Your employer is also entitled to hold your quality of work to the same standard as a non-disabled employee. If a part time schedule would NOT permit you to do all the essential functions of the position up to that standard, then shortening your schedule would NOT be a reasonable accomodation and barring a different accomodation that would work being provided, it would be legal to term your employment. Also, your employer is NOT required to give you the accomodation you want or that your doctor recommends as long as the accomodation they require is effective. So if they offer an accomodation that would be effective but would still require you to work full time, that is legal and if you refused it, they would have no liability.
I know this is confusing so if you need clarification, say so and I'll be glad to help.