Niantic has revealed that it plans to restore all lost stacked Research Reward encounters in Pokémon GO. The developer is also addressing low storage concerns by players. The official announcement from the development team is as follows:
Good news, Trainers! Over the next few days, we will be restoring lost stacked Research Reward encounters. Please note you will need storage space to catch these Pokémon. We know that storage is a concern and our team is working hard to address this. Thanks for all your patience.
Source: Niantic Support @NianticHelp