I've added a button to save the game as well as a "Last game save" indicator to solve any save-related issues.
I'm unsure about the UI not refreshing since I am unable to reproduce the bug, but I'm working on it.
Viewing post in Genesis (Warning: currently has lag issues) comments
No sure if this helps, but playing again... Noticed that the "Last save" time sometimes goes negative.
Edit to add: Sometimes, it goes back positive, and things continue okay. Other times, it stays negative--and as long as it is negative, other things are not updating. I can sometimes make it reset by clicking he "Save" button numerous times, but not always.