To remember:
Hyperconjugation is the stabilising interaction that results from the interaction of the electrons in a σ-bond (usually C-H or C-C) with an adjacent empty or partially filled p-orbital or a π-orbital to give an extended molecular orbital that increases the stability of the system. Further information.
The proposed systems to take into account.
Looking at the resonance structures (which is a synonym of mesomeric effect) of the propene
Resonance structures of propene http://image.tutorvista.com/content/organic-chemistry/hyper-conjugation-propene.gif
(source: tutorvista.com)
and acetic acid
Resonance structures of acetic acid http://nonsibihighschool.org/intbasch9_files/aceticFC.png
(source: nonsibihighschool.org)
Therefore, in hyperconjugation analysis you need to look at the position of the electron density. Not the vicinal hydrogen.
Moreover and with the aim to give a complete answer, the hyperconjugation of the acetic acid can be very well understood at here.