Should this fired deputy get his job back?

From the information presented in the article, no.

It's clear the man has issues with alcohol that he has not been able to manage. Moreover, his violation of the law should exclude him for at least five to 10 years, if not permanently.

 

It is nice in theory, and I agree with your belief. That said with all the abuse that departments have been taking over (at least) the last 10-15 years, morale is at an all time low, many good officers leave law enforcement altogether, departments are defunded, application rates fall, and as a result standards for Police officers are lowered so as to get officers.
The moral of the story is when you spend all your time complaining about and abusing the police, you end up getting the very police that you don't want.