Subversion SSL handshake failed and 408 error code

The 408 response is simply because openssl didn't ever send an HTTP request. It did the TCP connection and the SSL handshake but that's it.

The important parts of the response are:

Protocol  : TLSv1.2
Cipher    : ECDHE-RSA-AES256-GCM-SHA384
Verify return code: 0 (ok)

The 0 (ok) part means that as far as openssl is concerned, the SSL connection is fine. The certificate is valid and at least one cipher and protocol are supported.

But the error message from your bash script suggests that the SSL connection is not fine. My best guess for the reason is that the server has been upgraded and now no longer supports TLS 1.0 and TLS 1.1 and whatever your bash script is using for HTTPS requests doesn't support TLS 1.2. You can run a test for this by adding the -tls1 option to your openssl command.

If this results in something other than 0 (ok) then this TLS version incompatibility is most likely the problem.

It's also possible for the problem to be a mismatch of available ciphers. If you still get a 0 (ok) for TLS 1.0 then it might be worth looking in to the ciphers available at the server and the client.

It might also be worth looking at the last change made to the server or just trying to upgrade the client. (It's a shot in the dark but sometimes those work...)