I have a client that is in the middle of the same problem.
On my client's behalf, I contacted Network Solutions, and they told me that they've had latency problems with their servers. This would cause the time-outs from Authorize.net. (There is a 10-second time-out, which should be more than sufficient.) Network Solutions said the latency problem should be fixed in a few days. A few days later, I was still experiencing the same problem. That is, customers would try to make a payment and be told that there is a problem with the site, and I would get an email saying that the transaction timed out.
This time, I pulled the activity logs from Network Solutions and found out that there was no incoming connection from Authorize.net. Nothing. Nada. It wasn't a matter of latency; it was a matter of Authorize.net being blocked by a firewall at Network Solutions. Armed with this new information, I approached Network Solutions, and suddenly their story changed. They said that they had received some malicious traffic from Authorize.net and therefore blocked them in the firewall. However, for $70, they would pay a technician to resolve the situation in a few days.
I smell a rat. This is the latest in a series of issues I've experienced with Network Solutions. I told my client that I can switch him over to a more reputable ISP, like GoDaddy, in a few days. As soon as he gives me the go-ahead, it's adios Network Solutions.