We've only just recently got our online payments working again but had to move our website from shared hosting to VPS in order to do this.
The problem appeared to be the SSL/TLS handshaking which ensures the secure communication of data between our website and PayPal when reporting the success/failure of online payments. PayPal confirmed to me that they had changed their SSL certifications in August which I think initiated the problem. However, rather than telling me what had changed, they gave me a long list of standards describing how we should communicate. This was not very helpful and time-consuming, and it wasn’t obvious what was wrong. Eventually, with some help from our website's hosting company, we began to think it was something to do with a mismatch of “ciphers” which is part of this SSL/TLS handshaking process. This wasn't something we could change when using shared hosting so we switched to VPS. I then found out which ciphers are typically used as standard and discovered that our server was using some non-standard ones and it was appears to have been these which were upsetting PayPal. With VPS hosting I was able to remove those unwanted ciphers and our Payflow link started working again.
Hope that helps,
Stuart
