I haven't purchased a USB hub in about a year or so, so I might be a little behind on the technology there but...
I honestly have to wonder if the thing is really supports 4! 3.0 ports. Remember, the total speed of the entire topology can only be as fast as the single connection up-stream. Point being, you'll never get true 3.0 speeds at the same time on those four ports and more importantly, I have doubts that there is truly four 3.0 ports at all.
USB Hub controllers are generally made with four down and one up stream port. This is why you'll usually see USB hubs of 4->7->10->13 variety*. When it comes to the USB controllers inside the hub, they are typically of the 4-port variety. There are 2 and 7 port controllers but not in the 3.0 spec from what I've seen. So a typical 7 port hub sports two 4-port controllers in a star topology inside. A 10 port features three, 13 has four, and so on. A 28 port hub would feature a whopping 9 controllers! I can't really figure how one can have four 3.0 USB ports. At best, at least one port would be used up to gain the additional 2.0 ports. At worst, the 3.0 controller is farther down the chain
attached to the 2.0 port, negating
any 3.0 speed boost at all.
Knowing how the hubs are constructed is kind of important. IIRC, there is a limit of five hubs that can be chained in a row with an exception. This translates to 7 tiers of connections. So your root hub (inside the PC) counts as tier 1. Then that 28 port monstrosity counts as tiers 2, 3 and 4 (as near as I can figure). So that's four hubs total. If you attach simple devices, like some keyboards, you should, in theory, be OK since it would occupy tier 5. However, if you attach compound devices, they must exist no later than the 4th ub. I don't know what each of those devices you listed are internally or how they appear on the USB device listing but I would bank that at least a few of those devices are seen as compound devices. For instance, the iPac4 is probably seen as a compound device purely from the standpoint that it can be reconfigured programmatically and, I'm reasonably sure, that there's nothing in the specs that allow a simple keyboard such a feature. Even worse, a device could have a hub inside
and be a compound device.

It's easy to exceed the hub limits if you're working at an extreme configuration.
In addition, I've seen some sources cite the Intel xHCI USB controllers are limited to ~96 end points (not quite the 127 devices often advertised no matter how you slice it). Again, I don't know what that hardware you have looks like on the USB bus, but if each device is a complex device seen as say.... 8 end points (I believe my wife's pro camera and our Androids appear that way), then.... I don't have enough fingers.... 12? pieces of hardware multiply by 8 and... carry the six.... or is the one?
You get the point..... 96 end points... Add one more device and you get that message. (I can't quite remember if a HUB controller counts as an endpoint)
It could be one, or it could be the other or a mix of both explanations. I've seen discussions where the error message appears with as few as 4 devices (audio for instance) or 10 input boards (like iPac or KeyWiz's) so it may not even be the above explanations I've given but something else entirely.

Using smaller hubs on multiple ports seem to help like eds mentioned, though it doesn't work for all.
The problem is known, but not entirely understood. I believe the flight sim guys have been squawking about it and I spotted a post that linked to this at Microsoft:
http://answers.microsoft.com/en-us/surface/forum/surfpro2-surfdevice/not-enough-usb-controller-resources/0c5d9766-a76e-4abf-a511-bae04bbe6328?page=2.
The solution is interesting. Disable the 3.0 xHCI controller and install/use the 2.0 speed (EHCI) drivers. Read the Caveats though, you might not like them. But if you're running Windows 7 or less I see no problem trying the solution since well, why would you need 3.0 speeds on any of those devices?
Good luck.

* There are 6, 8 and 9 USB hubs but they're oddball cases. For example, Amazon lists an 8 port USB hub intended to recharge 8 iPhones with the ability to upload new "charge profiles" whatever the ---fudgesicle--- that means.