Hi Sergey,
Thank you for the report and the sample scene, and apologies for the long delay.
This is now fixed in Ornatrix for Cinema 4D. The Ground modifier no longer changes the shape of spline based hair when a project is reloaded. The fix will be included in the next Ornatrix C4D build.
For any scene you saved before the fix, apply your detach and re-attach workaround once in that build and then save. After that the grounded shape is preserved on every reload, so you will not need to repeat it.
Thanks again for helping us track this down.