Can a teacher to refuse to follow their late work policy?
I doubt anyone can state conclusively that it is wrong for a teacher to change their policies in the middle of the semester. However, I think many can agree that a teacher does not want to be perceived as whimsical or mercurial by their students. If a teacher develops a habit of arbitrarily changing policies in the middle of a course to the detriment of students it can create a lot of ill-will between the teacher and the students. 

Sometimes it is necessary to make changes. Examples include a true oversight by the teacher that needs to be addressed, obvious abuses by students of a policy, etc. Becoming more lenient is always popular while become more stringent should be in response to inappropriate behavior.

Whenever a change is necessary it must be communicated to the class clearly with some form of explanation. This is as a courtesy to maintain a productive learning environment. If this is neglected students will search for ways to fight against what they believe is unfair changes through such as methods as complaining, low course evaluations, or even academic dishonesty.