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A person is permitted to request and take FMLA leave any time they need to be off from work due to a serious health condition. If you need periods of time from work, you'll be eligible.
To be eligible though, you have to have worked at the location for at least 12 months, you have to have worked at least 1250 hours in the last 12 months, and the employer has to have at least 50 employees within 75 miles of where you work.
You can find the text of the Family Medical Leave Act in the Code of Federal Regulations, here: Code of Federal Regulations, 29 CFR 825.
If your employer was aware that you were missing time from work due to a medical issue, they should have informed you of the right to use FMLA instead of using the attendance issue against you. They technically have already violated the FMLA then. Your employer should be responding quickly to this request and if they do not, you need to file an enforcement action against the employer with the Department of Labor.
You can have a doctor certify you for intermittent use of FMLA, based on the need to take periods of time off on a very short notice basis. You still are only entitled to 12 weeks of time off that is protected under the FMLA, but it doesn't have to be taken in well-defined and pre-planned blocks. You can take it in 15 minute increments even, so there is no legal issue with fragmenting it.
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