An active cable has an amplifier built in, but it does not have a power supply for it. Your computer's firewire port therefore has to supply the power. That shouldn't be a problem as long as the cables are high-quality, you're only using one extension segment, and your audio interface isn't also relying on firewire power. You could avoid any potential power-related issues by using a powered hub as a repeater rather than an active cable (but it'll be more expensive).
The spec says you can go over 200' (using multiple 15' segments with powered repeaters). I've
heard of people going up to 60' using active cables, but that's just hearsay. The longest I've gone is 15' with a single cable, and initially I had a LOT of issues with even that length. Those issues turned out to be the result of having bought a cheap generic cable because the one that came with my interface was too short. After replacing it with a high-quality cable the problems went away. The moral of that story is don't scrimp on cables.