Is there any way to save breakpoints in IntelliJ and restore later?

You cannot save/restore breakpoints in IntelliJ, but if you want to work with different "groups" of breakpoints in different situations without having to enable/disable or delete them one by one, you can do that in the current version (IDEA 2016.3.1).

You can create named groups of breakpoints and enable/disable them as a group with a single click. https://www.jetbrains.com/help/idea/2016.3/working-with-groups-of-breakpoints.html

This feature is currently not available (not even in Intellij Cardea EAP).

However, there is an IDEA feature request up for this: http://youtrack.jetbrains.com/issue/IDEA-15540.

Want to up-vote the feature request ?

You can find all breakpoints in project-dir/.idea/workspace.xml -> <component name="DebuggerManager">. You can save their manually.

On Android studio you can select multiple break points -> Right click -> Move to group -> new breakpoint group.

After this you can enable/disable entire group just like importing previously saved breakpoints.