If you unlock all abilities, save the game, then close the trainer, the abilities will remain (because the game writes the mutation state to the save file). However, if you then try to "unlock" them again with the trainer off, they might lock. Always launch the trainer before loading the save.
Unlocking Ultimate Power: The Definitive Guide to Prototype 2 Trainers and Ability Unlocks prototype 2 trainer unlock all abilities
The trainer ZIP file includes: