Since this is issue is only resolved during the restart of the server and not during the restart of the services, it would appear that the connectivity is being broken between the server itself and the LDAP server. I have seen this in the past where a LDAP load balancer was being introduced into the system and this was what appeared to be the culprit as removing the load balancer and then entering the various LDAP severs directly (essentially bypassing the LDAP load balancer) resolved the issue and stopped the random disconnects for that particular client.
If you are using ALM12,2x or newer versions the capability to add in multiple LDAP server directly into the LDAP settings is now possible and that may resolve your issue if this is applicable. Otherwise I would look into the path through a tracert or some IT assistance tools paired with the Windows and various logs to see when and what may be causing the disconnect/loss of connection with the LDAP server.
Hope this helps,