Why does iTunes or App Store asks for my password every single time I update an app?

This happens because you probably have Restrictions enabled on your iPhone, under Settings > General, and have set up your 'Require Password' interval to 'Immediately'. Here's the easy fix:

Go to General > Restrictions > Require Password and choose 15 minutes.

That's it, from now on you'll be asked for your Apple account login less often.