My Samsung A3 won't save new contacts. Nor will it delete linked contacts. What can I do?

[AC Question]

My Samsung A3 won't save new contacts. Nor will it delete linked contacts.

There appears to be a major glitch with the contacts application with my Samsung A3 - a relatively new phone. As a general rule it does not allow me to save new contacts and occasionally doesn't save updating existing contacts.

I am also having trouble deleting contacts that are linked to a couple of applications.