  With the greater power to infer the state of stellar interiors provided by
asteroseismology, it has become possible to study the survival of initially
convective cores within stars during their main-sequence evolution. Standard
theories of stellar evolution predict that convective cores in sub-solar mass
stars have lifetimes below 1 Gyr. However, a recent asteroseismic study of the
star Kepler-444 concluded that the initial convective core had survived for
nearly 8 Gyr. The goal of this paper is to study the convective-core evolution
of Kepler-444 and to investigate its proposed longevity. We modify the input
physics of stellar models to induce longer convective-core lifetimes and vary
the associated parameter across a dense grid of evolutionary tracks. The
observations of metallicity, effective temperature, mean density, and
asteroseismic frequency ratios are fitted to the models using the BASTA
pipeline. We explore different choices of constraints, from which a long
convective-core lifetime is only recovered for a few specific combinations:
mainly from the inclusion of potentially unreliable frequencies and/or
excluding the covariances between the frequency ratios; while for the classical
parameters, the derived luminosity has the largest influence. For all choices
of observables, our analysis reliably constrains the convective-core lifetime
of Kepler-444 to be short, with a median around 0.6 Gyr and a $1\sigma$ upper
bound around 3.5 Gyr.
