How does the aspect ratio of the vertical stabilizer affect stall speed?
Generating lift creates downwash. Downwash reduces the effective angle of attack:


Source

A high aspect ratio reduces the downwash and thus also its reducing effect on the effective angle of attack.

Therefore a high aspect ratio wing will experience a higher $\alpha_{eff}$ than a low aspect ratio wing at the same angle, and thus stall earlier.

The same happens with the rudder, but then with $\beta$ instead of $\alpha$.

EDIT: clarifying alpha - beta similarity

So, in the case of sideslip, we have the following situation:



Source

See the similarity between the $\alpha$-image above, and the $\beta$-image.
The mass flow changes direction, and leaves the end of the rudder (more or less) parallel to the rudder chord line. This deviation in airflow direction causes the force to the left.

So for a normal wing ($\alpha$-image), flow enters straight, leaves going down (downwash) and as a consequence the wings give a force up. 

For the rudder ($\beta$-image), the flow enters straight, leaves going to the right (downwash, but then sideways) and as a consequence the rudder give a force to the left.

About the stalling, stalling is not limited to the wings, also rudders can stall if the maximum effective angle they experience is above stalling angle ,and the force generated suddenly drops.

If we compare two rudders both with the same airfoil and the same $\beta_{eff_{stall}}$, say 10°.
The $\beta_{stall}$ will be given by:

$$ \beta_{stall} - \beta_{downwash} = 10° $$ 

If the $\beta_{downwash}$ is 4° for the low AR wing, and 2° for the high AR wing, it will mean the low AR wing will stall at a $\beta$ of 14° and the wing with the high AR will have a $\beta_{stall}$ of 12°.