What you are doing by leaving for short periods of time is correct!! They will always whine when you first leave and when they hear you come back, thats natural! If they know you are standing outside the door listening and they hear/smell you yes they will continue to whine BUT may not be doing it after you leave
Now, is your pup in a crate and does your pup have something to keep occupied with? Some safe toy to chew on?
Also, the clock is a great idea, just keep it outside of the crate...you can also put on a radio 'low' on soft music...very mellow type music...elevator/classical.
Before you go, pup gets a walk, if even a short one and a treat and 'good doggie praise' for going in the crate.
When you come back, praise praise again and reward BUT it sounds like you need to leave for atleast 1/2 hour to give the pup time to calm themselves down.
What may be happening is that the pup senses you are still nearby, and it's whining is 'bringing' you back home so it's being rewarded and reinforced that the more it whines the more you'll come back!!
Stay out a wee bit longer 1/2 hr to 45mins and I am sure over time this will change. What type of pup and how long have you had, where did ya get from and do tell us her lovely name!