Michael,
Do you have any debug logs of the disconnects? If so, what do they indicate? Do they contain any timeouts?
We have come across a similar issue recently, though probably different to yours, but there may be something in our experience that can help you.
There has been a change (effecting the test/development installation only) to a new firewall that results in connections to the database and the ldap server being timed out by the new firewall without sending messages to the JDE server, the ldap server or the database server (which the current production firewall does) and there is no option to change this behaviour. This situation is compounded by the fact that the JDE software assumes the connections are still open (without doing a "heartbeat" check) and JDE waits for a timeout. The result is that signing on to JDE sometimes requires 2 or 3 attempts and each attempt can take 5 minutes or more. Granted, in a production system, because of the much higher level of activity, it would not be as much of an issue, but it still would be an unacceptable situation. Setting the timeout on the ldap server to be less than that on the firewall has helped, but the same action with the database or database server does not seem to work. One work around that we have considered is to run a short UBE on the JDE Scheduler every 2 hours to prevent the new firewall from timing out the connections.