Why is Google Chrome not saving proxy username/password?

To save login and password, go to the Options, and Personal Stuff. Select the option Offer to save passwords.

After, close the browser, open again, and put your user and password. To verify if it works, close and re-open one more time. If Google Chrome loads the proxy login screen, with user and passwords already loaded, this workaround worked well.

Edit: in newer versions of Chrome, it should use your system proxy settings by default. Alternately, there is a command line option --proxy-server=host:port that should work.

Previously: Click the little gear icon in the upper right corner, select "Options". Go to the tab "Under the Hood", and click "Change Proxy Settings". Make sure "Manual Proxy configuration" is selected and fill in your proxy. Click the "Details" button to enter your user and password.

I had the same when I have upgraded my chrome to version 41.

The easy way to get rid of this is by adding one of these Chrome extensions "Proxy Auto Auth" or "Proxy Helper". Just add one of these extensions to your chrome and save your proxy credentials. After that you wont be asked for entering your proxy details again and again when ever you open the chrome.