The stability of ions in aqueous solution depends on their electrode potentials and electronic configurations, particularly considering Crystal Field Theory (CFT).

1. Chromium ($Cr^{3+}$): Electronic configuration is $[Ar] 3d^3$. In an aqueous solution, water molecules act as ligands creating an octahedral field. The $3d$ orbitals split into $t_{2g}$ and $e_g$ sets. The $3d^3$ configuration results in a half-filled $t_{2g}^3$ level, which provides significant extra stability (Crystal Field Stabilization Energy) . Consequently, $Cr^{3+}$ is highly stable.
2. Manganese ($Mn^{3+}$): Electronic configuration is $[Ar] 3d^4$. It is a strong oxidising agent because it tends to gain an electron to form the stable half-filled $3d^5$ configuration of $Mn^{2+}$ . Thus, it is less stable than $Cr^{3+}$.
3. Titanium ($Ti^{3+}$): Electronic configuration is $[Ar] 3d^1$. It is a reducing agent, tending to lose an electron to form the stable noble gas configuration of $Ti^{4+}$ ($3d^0$).
4. Vanadium ($V^{3+}$): Electronic configuration is $[Ar] 3d^2$. While relatively stable, it does not possess the special stability of the half-filled $t_{2g}$ shell found in $Cr^{3+}$.