Pearson, the maker of the MAT, does not explicitly state how many times you can take the MAT. What information they do provide is available in the Scoring FAQ and the Candidate Information Booklet. Here is some general information about taking and retaking the Miller Analogies Test.
So how many times can I take the MAT?
There are multiple forms of the MAT. Each form has a different set of questions; although, each form is scaled to be relatively similar in difficulty. Obviously, if there was only one form of the exam, students would be able to share the questions among themselves and the exam would soon be useless.
Pearson states that a student may only take the same form of the MAT once in a 12 month period. In theory, as long you take different forms each time, you could take the MAT multiple times in the same year with no specific waiting period between exams. I have not found an official statement as to how many MAT forms there are. But it is common for students to take a graduate exam 2-3 times, so I feel confident in assuming Pearson has probably developed at least five different forms (likely more). Students should then be able to take the exam at least five times in a 12 month period.
Informing the test center
If you do decide to retake the exam, make sure you contact your test center and explain that you have taking the exam previously. They need to ensure that you are not tested with the same form twice.
Also, the score report provided by Pearson includes your testing history. This means that how many times you have taken the exam and the score you received each time will be visible on the score report. Again, it is extremely common for students to take graduate exams 2-3 times. However, if you intend to take the exam 3+ times, be aware that the school will be able to see that.