WebDAV server using IIS: HTTP error 412 - iis

Question

I'm setting up a WebDAV server in my Windows 7 desktop, using IIS 7.5. The aim is for a WebDAV client app in my Iphone to be able to access and sync a series of files in a given folder in the PC. It's all in my own home network, and I'll be the only one syncing files.
Anyway, I've set everything up, but here is something really odd:
If I create a file in my Iphone, and then sync it to the Windows desktop, and then delete it in my Iphone... it deletes the file in the Windows desktop the next time I sync, as it should.
But if I create a file in my PC, sync it to my Iphone, and then delete it in my Iphone, the next time I sync it won't delete the file in the PC. It will return the HTTP error code 412 (Precondition failed).
I have enabled tracing in IIS, and looking at the request headers, I don't see the WebDAV client sending any precondition. Here is what it says:
Data about the HTTP request:
SiteId 1
AppPoolId DefaultAppPool
ConnId 1610612964
RawConnId 0
RequestURL http://192.168.1.111:80/Notebooks/filename.txt
RequestVerb DELETE
Request headers:
Headers Connection: keep-alive
Content-Length: 0
Accept: */*
Accept-Encoding: gzip, deflate
Accept-Language: es-es
Host: 192.168.1.111
If-Modified-Since: Wed, 07 Oct 2015 19:37:37 GMT
If-None-Match: "1ab8c9f371d11:0"
User-Agent: Notebooks 8.1.2 ( iPhone; iOS 8.4.1; es_ES)
And here is the only thing that the module says in its warning message:
ModuleName WebDAVModule
Notification 128
HttpStatus 412
HttpReason Precondition Failed
HttpSubStatus 0
ErrorCode 0
ConfigExceptionInfo
Notification EXECUTE_REQUEST_HANDLER
ErrorCode The operation was correctly completed. (0x0)
The above were the errors shown in IIS tracing. As for the regular Web server log:
192.168.1.230 - (my PC name) [07/Oct/2015:23:13:59 +0200] "PROPFIND /Notebooks/filename.txt HTTP/1.1" 207 509
192.168.1.230 - (my PC name) [07/Oct/2015:23:13:59 +0200] "DELETE /Notebooks/filename.txt HTTP/1.1" 412 1738
I have been in touch with the developer of the Iphone WebDAV client, and he says that, in his experience, this tends to suggests permission problems, but I have checked the permissions of the files in Windows, and they are fine. By this I mean that I check the files that I can delete from WebDAV, and then the ones that give me the 412 error... and both have identical permissions.
What else could it be?