Just thought I would update on a discussion from last week as there was conflicting info flying around.
There IS a re-entry permit office at the border with Laos in Nong Khai. It's open every day from 8.30 to 16.30 (note this is different from the opening hours of the border itself). It's located on the left, just as you enter the border hut (where you stamp out of Thailand), but before you actually get stamped.
I assume the procedures are the same as everywhere else. It looked pretty quiet yesterday evening when I passed by!
TLDR : Answer Summary
There is a re-entry permit office at the Nong Khai border with Laos, open daily from 8:30 AM to 4:30 PM, located just before the immigration stamp-out point.