With Photosmith open on your iPad Air, double-click on the Photosmith Publish Service header in Lightroom, then click the Search button. Photosmith on your new iPad Air should be shown in the drop down. Then click the Save button. Choose to Re-Publish your photos... it will take a little longer than not Republishing, but it's "safer."
The key is making sure the Publish Service is set to recognize the "new" installation of Photosmith on your new iPad, and saving those changes in the Publish Service configuration window.