When doing some more testings, I found out that SSHD seems to have some issues to handles files with specific size. I've created files ranging from 50 to 400 bytes and it looks like that starting at 71 bytes, an exception is generated by SSHD itself (before any processing by the subsystem).
It crashes with an EOFException on the InputStream.
I've attached such a file. I've transfered bigger files that had absolutely no issue. I did try to debug it but I could not fix it. Now I just hope that someone else could find a lead to a fix.