When will they be in touch with me because this is a production problem. I was hoping to find a solution here from other users as well.  

There isn't enough information in this thread or your post to hazard a guess. The message is reported by the Laserfiche Server if it takes more than 1 second to establish a connection with SQL Server. There could be various reasons why the connection between 2 machines is slow, the message indicates the most common one. Given your server specs it's possible that it may be a network issue rather than load on SQL, but we can't rule it out.

Please work with your solution provider to troubleshoot the issue with Laserfiche Support.

The connection taking a long time is just a symptom, so the resolution is going to depend on the underlying cause. In the original post, performance is uniformly bad, so that at least rules out that it's something specific to establishing a connection. From the Laserfiche server, all it knows is that responses aren't coming back as quickly as they should. The obvious places for the time to be lost is 1) queries are executed slowly, and if so the most likely cause is that the server is overwhelmed - this is what the error message gets at - or 2) general network slowness between the Laserfiche server and the SQL server.

If load is light on the SQL server, and a tool like Profiler indicates that the queries are executing quickly, then you're probably looking at a network problem. In that case, you'll fallback on the typical troubleshooting process for that: ping, Wireshark, firewall logs, testing latency from/to other machines, etc.