FAFSA only determines your ELIGIBILITY for Federal and other aid. FAFSA does not determine what or how much aid you will actually receive - the financial aid office at your college determines that. You can fill out the FAFSA form indefinetly, however, your college may put some limits on how many years and how much aid you will receive. Note that there are some limits on how much you can borrow in the form of student loans - these limits are set by the federal government, and can be set lower by your college, but not higher.
Here's an example: You fill out the FAFSA and it gives you a zero (O) EFC (Estimated Family Contribution). Most people assume that means they will get a "free ride" - meaning they won't have to spend a penny of their own money on college. This isn't true, but the amount of your own money, and the amount of loans and/or grants you receive, will be determined by the college and can vary greatly from college to college. Say you have three different colleges, all with an estimated annual cost of $12,000 a year. College 1 will look at that zero EFC, give you $4050 in Pell Grant and student loans for the rest. College 2 may look at that zero EFC, give you $4050 in Pell Grants, $2500 in State Grants, $3000 in institutional grants (money from the college's own scholarship funds) and the rest in student loans. College 3 may look at that zero EFC, give you $2000 in Pell Grants and the rest in student loans. All three will award you differently, even though your FAFSA form information is exactly the same.
To determine how long you can receive aid through your college you have to talk to the financial aid office at your college. Each has different policies, and most of them revolve around something known as "satisfactory academic progress." As long as you are proceeding towards eventually graduating, are maintaining a minimum GPA (usually 2.0 or above), and taking classes mostly geared towards your degree, you can usually take as long as you want to finish your degree. If you are taking only one class per semester that applies directly towards your degree and three other classes that are only elective, and continue doing so for several years, they may question your progress and suggest you buckle down.
I do know a woman in my college who is in her 8th year, with at least two more years to go at her present rate of taking classes, before she will get her bachelors. She takes only two classes per semester, one towards her degree, one towards her general education requirements or elective requirements. She is, of course, stretching things out quite a bit... but she is also making "satisfactory progress" so continues to receive aid, albeit not as much as she would receive if she went full-time. The school has no problem with this because she is progressing towards her degree. (She has six children and also works part-time, but the "real" reason she is taking so long is because its a perfect excuse to take a break from the kids every day! "It's Mommy's study time" is her favorite line!)
If you are currently in school, receiving financial aid, and making satisfactory academic progress, you can continue filling out the FAFSA every year. The aid you actually receive is determined by your college, and how long they will assist in funding your education is ultimately up to them.
I'm a fifth-year senior, who will begin my PhD studies in the Fall. No problem receiving aid in my 5th year, and definetly no problem receiving aid for the next five years of my PhD program.