Is there a free LaTeX IDE that keeps indentation when word-wrapping?

Did you try out TexMakerX http://texmakerx.sourceforge.net/? It is free, has a very, very powerful editor, is available for different platforms and it should do what you want (if I understood your question correctly, see example screenshot).

Disclaimer, it doesn't answer the question. But I think is fine to have this info here.

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And yet another one: TextMate.

Here is the question in Superuser.SX and here the link to the list.

Quote:

Note: This applies only to TextMate 2.

1. On the menu bar, select Bundles › Edit Bundles.

2. Within the Bundle Editor display, select LaTeX › Settings. Once here, a list of preferences indicated by a white P on a gray circle is seen.

3. On the menu bar again, click on New or press command-N. From the Bundle Editor display, TM will prompt you to choose what to create: bundle, command, setting, grammar, etc.

4. Click setting. An untitled setting will appear in the Bundle Editor window.

5. Name the new setting. I used Soft-wrap indent.

6. Select the new setting if not already selected.

7. In the text field, paste

   {   indentedSoftWrap = {
           match = '\A[ \t]*';
           format = '$0';
     };
   }
   

   This enables soft-wrap indent + 1 extra tab.

8. If you wish to restrict this to a certain scope, it can be done in the drawer next to "scope selector." Leaving it blank will enable soft-wrap indentation for any text file.

9. Save the setting by pressing command-S and close the Bundle Editor.

10. Make sure soft wrap is enabled. (View › Soft Wrap). It might be necessary to reload any open files for the setting to take effect.

Kile has this feature in Linux, and the authors claim that it can be run under Windows. I find this feature important as well!