Short answer: no. There is no built in functionality in TestComplete to indicate that, if a test case is failed, to re-run it.
In truth, this is a feature/functionality of Test Management software like QA Complete or Jenkins... to identify failed test cases and then, with a set of clicks or whatever, re-run them. TestComplete executes the tests and reports on them, other apps do the management of what needs to be re-run.
Long answer: If you write enough code, you can do this. You would need to, somehow, write your tests in such a way that, if they "fail" (and you would need to clearly define a "failure" in code so as to make sure you properly identify it), you would somehow mark the test to be rerun (put the KeywordTest identifier or script routine reference into some sort of Array) and then write code to go through that list of tests and re-execute them. It can be done. As I'm fond of saying, you can automate ANYTHING given time, resource, energy and skill.