Multi-part answer. Appears 2) is what you may need.
1) About what @WayneSchulz said, since you have potentially 60 connections to the MAS App Server which is running on the server's desktop (not as a service), you should be more focused on possibly changing the 2nd number (desktop heap size) in the SS-3003 registry hack. But if you're on Server 2008 or higher, it is probably at 20480 which is high enough.
2) Ergo, more likely you need to check the box for Spawn Task from Application Server in User Maintenance / Preferences for all users and with everyone out of the system.
3) What @JaneCavanaugh said is very relevant but most likely you would get the error right off the bat as soon as you open the 1st task off the Launcher. You wouldn't have to wait until the peak time of the day for it to happen. Your options for that would be:
a) Enable Spawn Task from App Server as it requires less inbound ports to be open if Windows Advanced Firewall is being used),
b) Open a broad range of inbound ports for Windows Advanced Firewall
c) Disable Windows Advanced Firewall on the server