We perform a statistical assessment of solar wind stability at 1 AU against ion sources of free energy using Nyquist's instability criterion. In contrast to typically employed threshold models which consider a single free-energy source, this method includes the effects of proton and He^{2+} temperature anisotropy with respect to the background magnetic field as well as relative drifts between the proton core, proton beam, and He^{2+} components on stability. Of 309 randomly selected spectra from the Wind spacecraft, 53.7% are unstable when the ion components are modeled as drifting bi-Maxwellians; only 4.5% of the spectra are unstable to long-wavelength instabilities. A majority of the instabilities occur for spectra where a proton beam is resolved. Nearly all observed instabilities have growth rates γ slower than instrumental and ion-kinetic-scale timescales. Unstable spectra are associated with relatively large He^{2+} drift speeds and/or a departure of the core proton temperature from isotropy; other parametric dependencies of unstable spectra are also identified.