Let's start with what POAC, (also known as law of conservation of mass) really talks about,
Within a chemical reaction, no new atoms are created or destroyed. More formally,
$$\sum{m_\mathrm{before\,rxn} = \sum{m_\mathrm{after\, rxn}}}$$
Moving onto what you have done
Now, by the Principle of Atom Conservation on vanadium, we get,
$$n_\ce{VO} = 2 \times n_\ce{V2O5}$$
$$\implies 2/67 = 2\times n_\ce{V2O5}$$
This is correct (well kind of correct). However, this makes one assumption that doesn't really exist in this scenario. It assumes that all the $\ce{VO}$ reacts within the reaction. Which unfortunately doesn't happen here.
Taken from Rafael L's comment, the right method to do this (and the most accurate method) is as follows
[...] convert the masses of $\ce{VO}$ and $\ce{Fe2O3}$ to moles, figure out which is the limiting reagent (balanced eqn: $\ce{2VO + 3Fe2O3 → 6FeO + V2O5}$), then calculate the moles of $\ce{V2O5}$ produced and convert moles of $\ce{V2O5}$ to mass.
Now, following this, we see the number of equivalents on $\ce{VO}$ and $\ce{Fe2O3}$ are as follows,
$$n_\ce{Fe2O3} = \pu{0.03593 mol} \implies \mathrm{equiv}_\ce{Fe2O3} = \pu{0.011979 eq}$$
$$n_\ce{VO} = \pu{0.029850 mol} \implies \mathrm{equiv}_\ce{VO} = \pu{0.0149250 eq}$$
From here, you can notice that the amount of $\ce{Fe2O3}$ that reacts is more than the $\ce{VO}$ but the number of equivalents is less. What this implies is that there is some $\ce{VO}$ left over. The rest is just multiplication.
[...] doesn't then POAC fail entirely? I used it many times which involved such reactions.
The answer to this question is no. POAC still holds. It's just a bit more complicated. Let's check this with the formal definition,
$$\sum{m_\mathrm{before \, rxn} = \sum{m_\mathrm{after \, rxn}}}$$
\begin{align}
m_\ce{VO} &= \pu{0.395 g}\\
m_\ce{Fe2O3} &= \pu{0 g}\\
m_\ce{V2O5} &= \pu{2.180 g}\\
m_\ce{FeO} &= \pu{5.174 g}\\
\end{align}
\begin{align}
m_\mathrm{before\,rxn} &= \pu{7.75 g} \\
m_\mathrm{after\,rxn} &= \pu{7.749 g}
\end{align}
Therefore, both are approximately equal, and POAC holds.