Motivation: 31P magnetic resonance spectroscopic imaging (31P MRSI) is a powerful technique for investigating the metabolic effects of treatments for heart failure in vivo, allowing a better understanding of their mechanism of action in patient cohorts. Unfortunately, cardiac 31P MRSI is fundamentally limited by low SNR, which leads to compromises in acquisition, such as no cardiac or respiratory gating or low spatial resolution, in order to achieve reasonable scan times. Spectroscopy with linear algebra modeling (SLAM) reconstruction may be able to address these challenges and therefore improve repeatability by incorporating a segmented localizer into the reconstruction. Methods: Six healthy volunteers were scanned twice in a test-retest procedure to allow quantification of repeatability. Each scan consisted of anatomical localizers and two acquisition-weighted (AW) 31P MRSI acquisitions, which were acquired with and without cardiac gating. Five patients with heart failure with a preserved ejection fraction were then scanned with the same 31P MRSI sequence without cardiac gating. All 31P MRSI datasets were reconstructed with both conventional Fourier transform (FT)-based reconstruction and SLAM reconstruction, which were compared statistically. The effect of shifting the 31P MRSI acquisition field of view was also investigated. Results: In the healthy volunteer cohort, the spectral fit of the SLAM reconstructions had significantly improved Cramer-Rao lower bounds (CRLBs) compared to the FT-based reconstruction of non-cardiac gated data, as well as improved coefficients of variability and repeatability. The SLAM reconstruction found a significant difference in the PCr/ATP ratio between the healthy volunteer and patient cohorts, which the FT-based reconstruction did not find. Furthermore, the SLAM reconstruction was less influenced by the placement of the field of view (FOV) of the 31P MRSI acquisition in post hoc analysis. Discussion: The experimental benefits of the SLAM reconstruction for AW data were demonstrated by the improvements in fit confidence and repeatability seen in the healthy volunteer cohort and post hoc FOV analysis. The benefit of SLAM reconstruction of AW data for clinical studies was then illustrated by the patient cohort, which suggested improved sensitivity to clinically significant changes in the PCr/ATP ratio.