I also had the same problem and I this is how I solved it:
Open "Settings" -> "Build, Execution, Deployment" -> "Gradle".
In the "Gradle projects" section select your project.
"Build and run using:" is set to "Gradle". Select "IntelliJ IDEA" instead.
I don't know why this solves the problem and what consequences this may have (e.g., maybe you will have to manually run some gradle tasks each time you change forge version, etc), but this does allows you to use Hot Swap.