Many cellular mRNAs contain the modified base mA, and recent studies have suggested that various stimuli can lead to changes in mA. The most common method to map mA and to predict changes in mA between conditions is methylated RNA immunoprecipitation sequencing (MeRIP-seq), through which methylated regions are detected as peaks in transcript coverage from immunoprecipitated RNA relative to input RNA. Here, we generated replicate controls and reanalyzed published MeRIP-seq data to estimate reproducibility across experiments. We found that mA peak overlap in mRNAs varies from ~30 to 60% between studies, even in the same cell type. We then assessed statistical methods to detect changes in mA peaks as distinct from changes in gene expression. However, from these published data sets, we detected few changes under most conditions and were unable to detect consistent changes across studies of similar stimuli. Overall, our work identifies limits to MeRIP-seq reproducibility in the detection both of peaks and of peak changes and proposes improved approaches for analysis of peak changes.