Your comments

the https is served via Apache 2.2.x and the webdav backend is svn is 1.6.17 for the server I had the issue with.

I dug into this more with the admin of the server that was working for me and the one that wasn't.  Jumping to the end, the case that was not working looked like:

-propfind
-response did not indicate auth required (this svn server allows global checkout, but not checkin)
-put, without credentials
-401
-no request after the 401

We found on another svn and day combination that did work, global checkouts were turned off, and the response to the propfind indicated that auth was needed with a 401 response to the propfind.  When this happened, the subsequent put had credentials in it.

So, it looks like if Textastic responded to a 401 received after it sends the PUT, it would work with svn servers configured for global checkout and restricted checkin, such as the one I am trying to use.

Thanks!