This is true, remove the password on all of the computers you are putting on the new Homegroup, pick a host, then start from the beginning. Installing static IPs will solve your disappearing connection problem. After power is removed from a computer, DHCP (auto connect) has to reestablish all of your connections. Using static IPs eliminates this problem.
I'd love to hear about a better solution also. I ran into one that this did not work on. The new password will not go in. I enter the password, then the wait symbol on the password box never goes away.