We examine the impact of the strength of the E _ { R } = 127 keV , ^ { 26 } Al ( p, \gamma ) ^ { 27 } Si resonance on ^ { 26 } Al production in classical nova explosions and asymptotic giant branch ( AGB ) stars . Thermonuclear ^ { 26 } Al ( p, \gamma ) ^ { 27 } Si reaction rates are determined using different assumed strengths for this resonance and representative stellar model calculations of these astrophysical environments are performed using these different rates . Predicted ^ { 26 } Al yields in our models are not sensitive to differences in rates determined using zero and a commonly stated upper limit corresponding to \omega \gamma _ { UL } = 0.0042 \mu eV for this resonance strength . Yields of ^ { 26 } Al decrease by 6 % and , more significantly , up to 30 % , when a strength of 24 \times \omega \gamma _ { UL } = 0.1 \mu eV is assumed in the adopted nova and AGB star models , respectively . Given that the value of \omega \gamma _ { UL } was deduced from a single , background-dominated ^ { 26 } Al ( ^ { 3 } He , d ) ^ { 27 } Si experiment where only upper limits on differential cross sections were determined , we encourage new experiments to confirm the strength of the 127 keV resonance .