Using mRNA as a therapeutic has received enormous attention in the last few years, but instability of the molecule remains a hurdle to achieving long-lasting therapeutic levels of protein expression. In this study, we describe our approach for designing stable mRNA molecules by combining machine learning-driven sequence design with high-throughput experimental assays. We developed a high-throughput massively parallel reporter assay (MPRA) that, in a single experiment, measures the half-life of tens of thousands of unique mRNA sequences containing designed 3' UTRs. Over multiple design-build-test iterations, we have accumulated 180,000 unique measurements of mRNA stability covering unique genomic and synthetic 3' UTRs, representing the largest such dataset of sequences. We trained highly-accurate machine learning models to map from 3' UTR sequence to mRNA stability, and used them to guide the design of synthetic 3' UTRs that increase mRNA stability in cell lines. Finally, we validated the function of several ML-designed 3' UTRs in mouse models, resulting in up to 2-fold more protein production over time and 30--100-fold higher protein output at later time points compared to a commonly used benchmark. These results highlight the potential of ML-driven sequence design for mRNA therapeutics.