Polyploidy is increasingly seen as a driver of both evolutionary innovation and ecological success. One source of polyploid organisms' successes may be their origins in the merging and mixing of genomes from two different species (e.g., allopolyploidy). Using POInT (the Polyploid Orthology Inference Tool), we model the resolution of three allopolyploidy events, one from the bakers' yeast (Saccharomyces cerevisiae), one from the thale cress (Arabidopsis thaliana) and one from grasses including Sorghum bicolor. Analyzing a total of 21 genomes, we assign to every gene a probability for having come from each parental subgenome (i.e., derived from the diploid progenitor species), yielding orthologous segments across all genomes. Our model detects statistically robust evidence for the existence of biased fractionation in all three lineages, whereby genes from one of the two subgenomes were more likely to be lost than those from the other subgenome. We further find that a driver of this pattern of biased losses is the co-retention of genes from the same parental genome that share functional interactions. The pattern of biased fractionation after the Arabidopsis and grass allopolyploid events was surprisingly constant in time, with the same parental genome favored throughout the lineages' history. In strong contrast, the yeast allopolyploid event shows evidence of biased fractionation only immediately after the event, with balanced gene losses more recently. The rapid loss of functionally associated genes from a single subgenome is difficult to reconcile with the action of genetic drift and suggests that selection may favor the removal of specific duplicates. Coupled to the evidence for continuing, functionally-associated biased fractionation after the A. thaliana At-α event, we suggest that, after allopolyploidy, there are functional conflicts between interacting genes encoded in different subgenomes that are ultimately resolved through preferential duplicate loss.