I have found the cause of our problem.

M-Turbo deletes the all records which have the request path the same as a record in DB table 'core_url_rewrite' with 'options' "RP". Reason is preventing to cache the pages with option "Redirect Permanent". Unfortunately the request path of one of your records in 'core_url_rewrite' equals identifier of homepage. Therefore it is deleting during synchronization.

In fact, it is not necessary in this case. Homepage have privileged position among another pages and there is not need to delete it. We will fix it in next release.

Now, you can delete this record and redirect made by .htaccess rule.

thank you very much for your excellent support !