I'm using IntelliJ IDEA 2019.1.3 and it persist with the "Indexing All the Time" issue. But the worst part is not that, the worst is that every time it start indexing from scratch as if it were an "Invalidate caches/ Restart" command.
Can you just do it incrementally? And by incremental I mean just indexing new changed files. If by any chance you are already doing it that way, then could you fix it? Because it's not working.