If the "Recent Posts" widget on your Blogger blog has stopped working, it's obvious you are still using the corrupt "recent posts widget for blogger". The widget will probably be displaying "There was an error in this gadget" on your blog.
If you remove it from your blog and try adding it again, you will get a message that the gadget is broken, has errors and cannot be used until fixed.
I am currently using the Recent Posts Widget by Ziyush and it is working fine for me up till this very moment.
How To Add Recent Posts Widget To Blogger Blog
==> Log in to your Blogger dashboard
==> Go to "Layout"
==> Right on the sidebar, click on "Add Gadget"
==> Click on the "More Gadget" link. This will display gadgets contributed by third party developers for Blogger.
==> Type "Recent Posts" in the search box and hit the ENTER key
==> You will likely see three "Recent Posts" widgets from different third party developers.
==> Simply add the Recent Posts Widget by Ziyush
==> Customize it the way you want and SAVE.
View your blog and you should now see your recent posts displayed on the sidebar.
I hope it works for you.
You can also consider adding the floating share bar for Blogger blogs.