I don't think power is the problem. I have had 3 eSATA drives and an external USB drive operating at the same time.
I've been speaking with a Sonnet tech and he's trying to find out what the equivilant of a system.log is in a Windows based system - to see if he can tell what's happening when the conflict takes place.
This could simply be a problem of horsepower - maybe your system can't handle all the processing required for that many simultaneous heavy data movers. But I suspect it's more likely to be a resource conflict - the Firewire port and the 4 eSATA ports (on the Sonnet card) are overlapping and competing for use of the same IRQ or port number. If the drivers involved are too rigid, you may not be able to resolve this. On the other hand, if the drivers decide what IRQ and port they will use in the future at the time of their initial installation, you might try removing both devices' drivers and the actual cards (maybe can't for Firewire), then adding each piece of hardware and its driver installation separately so that the second device added "knows" certain resources already are assigned and does not try to use them. If Firewire first followed by eSATA card does not work, try re-doing in the opposite order. But this could be tricky because you might need to put eSATA devices on at least 2 (maybe all 4) card ports to "establish ownership" when its device driver is installed, THEN add in the Firewire port drivers.
There may be another solution to try instead. I have a vague recollection of a post on a related topic some months ago. The core of it seemed to be that certain system resources are assigned to ports and devices at boot time, and conflicts can arise if devices are connected AFTER booting. So try to have your eSATA devices AND your camera on the Firewire port connected AND turned on before the computer boots.