By default, you cannot save your SharePoint password. This is for security reasons. To allow your computer to save the password, add the SharePoint site to the Trusted Sites list...
- Navigate to and sign into the SharePoint site
- Click the Tools button (should look like a gear)
- Select Internet Options
- Click the Security tab
- Select the Trusted Sites icon, click the Sites button, Add the site in the box to the list
- Click the Close button
Next, set the Trusted Sites security level to 'Low'
- From the security tab, select the Trusted Sites icon
- Set the slider to Low (if you do not see the slider, click the Default Level button, then set to low)
- Click Apply, then close the window
- Refresh the site