  Kerr-cat qubits are bosonic qubits with autonomous protection against
bit-flips. They have been studied widely using driven Superconducting Nonlinear
Asymmetric Inductive eLement (SNAIL) oscillators. We theoretically investigate
an alternate circuit for the Kerr-cat qubit, namely Symmetrically Threaded
SQUIDs (STS). We perform the circuit analysis and derive the
Gorini-Kossakowski-Sudarshan-Lindblad (GKLS) master equation for the Kerr-cat
qubit attached to a thermal environment. We find that the lifetime time of the
coherent states ($T_\alpha$) of the Kerr-cat qubit is the same in both the STS
and SNAIL circuits for weak Kerr nonlinearity. However, the STS Kerr-cat qubits
have the additional benefit of being resistant against higher order photon
dissipation effects, resulting in significantly longer $T_\alpha$ even with
stronger Kerr nonlinearity on the order of $10{~\rm MHz}$. We also examine the
effects of strong flux driving and asymmetric Josephson junctions on
$T_\alpha$. Unlike the SNAIL design, we find a dip in $T_\alpha$ of the STS
Kerr-cat qubit for weak two-photon drive. However, we show that the dip can be
mitigated by applying a suitable drive-dependent detuning. With the proposed
design and considering a cat size of 10 photons, we predict $T_\alpha$ of the
order of tens of milliseconds even in the presence of multi-photon heating and
dephasing effects. The robustness of the STS Kerr-cat qubit makes it a
promising component for fault-tolerant quantum processors.
