A growing number of RNA sequences are now known to have distributions of multiple stable sequences. Recent algorithms use the list of nucleotides in a sequence and auxiliary experimental data to predict such distributions. Although the algorithms are largely successful in identifying a distribution's constituent structures, it remains challenging to recover their relative weightings. In this paper, we quantify this issue using a total variation distance. Then, we prove under a Nussinov-Jacobson model that a large proportion of RNA structure pairs cannot be jointly reconstructed with low total variation distance. Finally, we characterize the uncertainty in predicting conformational ratios by analyzing the amount of information in the auxiliary data.