How do I keep IntelliJ from closing my Editor Tabs automatically?

Change the Tab Limit under the Tab Closing Policy settings.

Open your IntelliJ settings: Select File -> Settings -> Editor -> General -> Editor Tabs.

Look for Tab Closing Policy -> Tab Limit and change the value to a higher integer.

You can also select to either close non-modified files first or less frequently used files first once your tab limit has been reached.