[Nozon]

This is out of my curriculum, but I just started wondering when I drew the reaction of an aldehyde and a secondary amine.

What if the adjacent carbon next to the α-carbon (β-carbon) in the aldehyde molecule does not have any hydrogen bound to it? How would the acid regenerate?

Would it go further out of the carbon chain till it found a carbon with an accessible hydrogen? and would the π-bound then move towards the α-carbon?

My best regards.
(Pictures drawn in order to support what I mean)

[Babcock_Hall]

In the top drawing, one of your arrows is drawn incorrectly.  I am pressed for time today; therefore, I cannot discuss it further right now.

[Nozon]

I see - you're right, arrow towards N's cation instead. 
It's okay - also just a question of interest.