App Store password keyboard
Close the app, double-click the home button to bring up the currently running apps, and hold down on the App Store until they bounce. Then kill it.

Then you can go back into it.

I've had a bunch of issues like this with the App Store app. sometimes I don't get the update button for apps, or no keyboard, etc. Restarting the app afresh sorts it out.

A total phone restart should also work.