Sounds like you have a corrupted windows store. This would cause updates not to run. This happens a lot more often than you would think. FYI, I am a professional computer geek - I fix problems all day for users. I have seen this and fixed a corrupted windows store many times on Windows 10.
There's a bunch of things i would try -- these steps take some time to run, all will help in fixing this problem.
Open This Computer, right mouse click on the C: drive, choose properties. Run the Disk Cleanup. I suggest running it twice (depending on what version operating system you have you may only be able to run it once). First time I would run it to clean up general files. Once it's done run it again and let it clean up the System Files. Delete everything. It might take a real long time to run if you have never run a cleanup before.
I would also reset Internet Explorer. Internet Explorer is a key component of Windows, even if you don't use it as a browser. Open Internet Explorer, go to the Advanced Tab, click on Reset (at the bottom).
I would also reset winsock and flush dns (these are network components). To do this: go to the start button, type command prompt, right mouse click on it and choose run as administrator, make sure to run as administrator, it will not work if you don't, then type:
Type ipconfig /flushdns then press Enter.
Type netsh winsock reset catalog then press Enter.
Type netsh int ip reset reset.log then press Enter.
Reboot.
Test. If it still doesn't work. Again open command prompt as administrator. Type: sfc /scannow. This scans all your windows system files for corruption and repairs them. This also will take some time. Reboot.
Test. If it still doesn't work, run the windows 10 update troubleshoot utility. You should be able to find it if you search the computer for troubleshoot updates. Make sure to click on advanced (on the left I think) and make sure the option to repair automatically is checked. Reboot once it's done.
Test again. If it still doesn't work. Try going to the start button and type wsreset, right-click the result and choose Run as administrator. Run all the test and reset everything. You might need to download/install from the app store, with all the versions of 10 I can't keep track of which ones have it and which ones have to go get it. This is the window store reset utility, fyi.
Reboot. Test again. It should be working by now.
