Rockbox asks for the maximum amount of USB power, 500mA (except on devices that support charging control, but that doesn't currently include the Fuze). If it's really a powered USB hub it should be able to provide this. Bus-powered hubs won't be able to (though many of them lie and claim they can anyway).
The stock firmware may ask for less, but it's unlikely; pretty much all devices ask for the maximum even if they don't need it, and for charging pretty much all devices draw the maximum even if they didn't ask for it
There should be a way to see how much the stock firmware is asking for: plug it in, then on Windows, go to control panel -> administrative tools -> computer management -> device manager. Find the USB hub in the list (it will be under "Universal Serial Bus controllers") and right click on it, hit properties -> power, and it should say whether the hub claims to be self-power or bus powered, how much power it provides per port, and how much power each currently connected device is asking for. None of this information implies that anyone involved is telling the truth, though, sadly: hubs often lie about their capabilities, and devices often exceed their stated requirements, and if this lying results in an actual physical current limit being exceeded somewhere, then you will generally see the behaviour you describe: a cutoff will disconnect the device, but then it'll reconnect again, and so on