Hello. I have completed the Deep Learning Specialization. Why did I lose access to my completed Cousera programming assignments?
Did you stop paying your subscription fee? The assignments are behind the paywall, even if you have completed them. The recommended thing would have been to download them before you stopped paying your subscription fee. There are some relevant topics on the FAQ Thread, q.v.
I believe/(or suggestion) the programming assignments should be available for the users who completed the assignments or course. For example - I have finished the course in 2018 and now I need to revising the course and also want to do assignments again and I have already paid money when I have completed the course.
Why should I need to pay money again for same course?
I don’t necessarily disagree with you, but I don’t make the rules. That is just the way the courses work: once you stop paying, you can no longer see the assignments. The thing to do is save your own copies by doing “File → Download (as notebook)”. You don’t assume that hard-drives never fail, right? You shouldn’t make the same assumption about websites. Three years is a very long time in the world of websites, as witness the fact that the courses were completely updated in April of 2021 and none of the previous assignments carried forward for anyone. Sorry, but that is the reality. As I commented above, you made an assumption and that assumption turned out not to be valid. That’s a big problem with assumptions in general. 
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I agree with that. I’ve download all the files when I completed one assignment, but one problem is the cells can not run using my computer’s jupyter, it says the kernel can not connect. Is there a way that I could run the assignments in my own computer?
I think either your local Jupyter instance is not correctly set up or perhaps there is some code in the notebook that needs to change to tell it to connect to your local Jupyter server instead of the Coursera Jupyter server up on AWS. I have not looked into how that works, but there must be documentation on Jupyter’s website about that.
We don’t have “official” instructions for how to run things locally, but here is a thread put together by a fellow student with lots of useful information. But as you’ll see by reading that thread, this is not a trivial exercise and requires some serious effort and problem solving ability to get it all to work.
To run notebooks locally on your computer, you also need to download all the data that is used in the notebook. This data is usually contained in folders, which can be found by clicking on File>Open. The location on the notebook where the data is used must have the correct path to the folder you downloaded.