Keychain does not show passwords after El Capitan upgrade

I had the same problem when using my wacom tablet with the Keychain. When using an actual mouse the problem does not occure. I found the following post that explained this problem in detail:

With the 10.11.1 update, Apple introduced a "security fix" that disabled the ability for non-physical devices to interact with the Keychain. You can see the details of this "fix" here (scroll all the way to the bottom of the page and look for CVE-2015-5943 for a full description):

About the security content of OS X El Capitan v10.11.1 and Security Update 2015-007 - Apple Support

You can confirm this being the issue with your machine if you view the system logs via the Console.app. When you click on "Always Allow", you should see the following in the logs:

Ignoring user action since the dialog has received events from an untrusted source

Basically, your click is being registered as a "synthetic click". In my case, this was because I was using Apple Remote Desktop (I also tested various other remote apps I use, like TeamViewer and iTeleport Connect, and all resulted in the same error in the logs).

So a solution to this problem is to use a physical mouse to interact with the Keychain.