I just upgraded from 1.7.5.0 to 1.7.5.1 yesterday without any problems. I went with the local directory update method.
The steps in detail:
- Download the latest 1-Click Upgrade v.4.6.0 within your modules catalog page.
- Download the latest prestashop_1.7.5.1.zip version manually, then extract all the files via FTP to admin/autoupgrade/latest.
- Go to 1-Click Upgrade and switch to Local Directory update method.
- Make sure your update/server speed is set to low.
From my experience this works the best because I usually face issues whenever I try to upgrade using the auto function or archive method. Im not sure whether it's because of PrestaShop or my host.