How long has it been since you started this job? I ask because if its only been a few weeks or months, they may be worrying that is is the norm for you and now you're causing issues. Others have to pick up your slack, etc. While I don't work in the same field, I do help in the hiring process for office staff at my job. No matter what area we are hiring for, it becomes a problem if someone is prone to being out often. We are a service industry and certain department's with high call off rates is a big no no. We know things happen, but anytime someone has called off excessively in the first month or 2, it usually indicates they won't be around long.

Never assume you can take unpaid time off in excess of a few days a year. Also never assume paid time off is able to be done on a whim 100% of the time. (This is industry dependent.)