Dead peer detection is a bit hit or miss. I start with it disabled and then add it in if the connection seems unstable. It only helps if the underlying network has problems though. (ADSL link that goes offline, occasional packetloss, that kind of thing). If you see constant dead peer detected messages in the logs you may try turning it off. If the connection is stable with it disabled then either the dead peer detection settings were wrong or something wasn't responding to keepalive messages as expected.
Scheduled connections do nothing for IPSec. This is for PPP style connections.
Setting the idle to 0 is the correct way to indicate the tunnel should stay "nailed" up at all times regardless of traffic.
So are your tunnels still renegotiating every few seconds? Have you had any luck isolating the problem? The last mention you said that both tunnels from one site were working properly but the connection between two other sites were still not working. Have you deleted the tunnels between those two problem sites and tried creating all new settings? Have you tried calling Netopia to have them look at the problem?