I would rather avoid going to Phuket Town to get a re entry permit, but I am not sure if immigration at Phuket airport is always staffed and able to issue a re entry permit?  Does anyone have first hand knowledge?

ever thort of phoning airport to ask???

If there is an international flight departing, there will be immigration officers on duty.  (May be obvious to me only.)

yes, when go to depart at immigration, just ask 1,000 / 3,800

single/multiple 
i think they charge you an extra 1-200 baht if u dont have all the paperwork

You can also go to Blue tree or Patong immigration offices to get re-entry permit. Im not sure about Patong, but at Blue tree immigration is not very busy.

If you have an international flight (you need a boarding pass to enter the immigration area), at the far left you will see a sign for re-entry permits. It's the same area where you pay an overstay fine.  

I have a Retirement Extension.
A week ago I left from Phuket Airport. For the first time in over 15 years I did not have a re-entry permit from Phuket IO.
I had all the documents prepared for the RE permit. 
At HKT Airport --- perfect service, in about 10 minutes everything was done, including exit stamp.
Even my TH wife was amazed at the great and attentive service. The IO- Lady brought the finished documents to us and explained the entry in the PP and asked for my verification.

I will never apply for RE entry permission in Phuket Town again, only at the airport.

 

Thanks for the helpful replies.  I definitely want to avoid Phuket Town and the wasted 3-4 hours, so these replies have been very helpful.