I dug into it with Process Monitor and I found a line (one column per line below)
21:06:17,6337584
TortoiseProc.exe
14144
CreateFile
[...]\.svn\tmp\svn-4F235F40
PATH NOT FOUND
Desired Access: Generic Write, Read Attributes, Delete,
Disposition: Create,
Options: Synchronous IO Non-Alert, Non-Directory File,
Attributes: N,
ShareMode: None,
AllocationSize: 0
Looking at my hard disk, I saw that there’s no tmp folder inside my .svn folder.
Creating the tmp folder manually resolved the issue.