Have you ever thought about not penalizing students for late work? In my classes, I generally provide due dates, however, there are no late penalties. The reason I do that is that this course is about learning to do something in a format that students may be completely unfamiliar in, number one. Secondly, my goal as a teacher is to make sure my students learn what I have to teach them and that they do quality work as they learn.
As a multimedia teacher, I knew that the blending of art and technology is difficult for many students. Usually, they came to my class with either technology skills or art background. Some, of course, came with neither, but that was a relatively small number. Because the class was usually evenly split, when we did technology-related assignments, one part of the class needed more time and vice versa with the art people. It didn't take very long to figure out that providing a window of time for the due dates for things, worked out well.
The other issue was wanting students to do their best quality work. If after the window closed, a student wanted to re-submit their work, I let them better their grade. Not many students took me up on that. Usually, it was the students who were going to become professionals in multimedia design who resubmitted. I think, though, it made them less stressed about doing the course work and I received beautiful work!
Ultimately, I want the students to tackle and learn the material. I believe that when students are confronted with difficulty in completing work, there could be a variety of problems going on. These "problems" often are issues that have come up for the student before and may be something they will continue to confront if they are not discovered and remediated. An online environment is often a great place for learning about learning to take place. A good example might be referring to a student having time management issues to an optional calendar development assignment.
I find myself working with students all the time over issues of their poor time management skills and/or their lack of resources. I ask students at the beginning of the course to let me know, in advance if possible, when they are having problems with due dates. By doing that, I usually find out what challenges many of my students face and contact over late work may be an opportunity for me to offer resources. Because time is flexible in an online class, you can play with how you deal with late work and other issues students have that set them back.
There is a good blog post by a K-12 teacher that is really worth reading on this topic and I highly recommend it (even for college and university professors). Link to Blog Post
Please take five minutes to read the blog post at the link above and then feel free to comment with your questions, ideas, and experience.