One of the disadvantages of extending the time limit of a standardized test is that it provides an unfair advantage to those students who received extra time. If every student completing the standardized test received the same time extension then it would be fair. A test like the SATs is taken by hundreds of thousands of students every year, and if one group of students got more time they would have an unfair advantage over other students completing the same test.
Another disadvantage of extending the time limit of a standardized test is that doing so could call the legitimacy of the test into question. The entire point of a standardized test, after all, is to standardize both the test and testing conditions, such as time, across the range of those taking the test. If time was unfairly extended for one group taking a standardized test then the results of that group should be disqualified, and may be by the testing authority.
Another admittedly mundane consideration when extending time limits for standardized tests is that scheduling conflicts may arise. Many standardized tests are scheduled at specific times in buildings and classrooms that have usage schedules. More rounds of the same standardized test, or other classes, may be scheduled. Students may also have commitments that a time extension would interfere with. Extending a time limit on a standardized test can potentially interfere with all these schedules.
There are, however, some situations in which granting time extensions on a standardized test is the right thing to do. Students with disabilities, for instance, may legitimately need more time to complete a standardized test, and in such a case giving a time extension on a standardized test might be necessary. These special cases might give the impression of unfairness and hence be a disadvantage, but some test takers do legitimately need more time to complete standardized tests.