The mobile appears to work normally when plugged directly into similar plug computers or into a laptop.
Does that mean that when you plug the phone into a USB port that is part of a desktop or laptop, it works fine all the time? You never see this dodgy behavior when it is NOT plugged into this hub? Have you ever plugged the phone's USB cable into a different external hub?
That right there is kind of telling. If the phone never exhibits this behavior when plugged directly into the computer, changes are good that it is neither the phone nor the cable itself that are at fault. This would point to the hub.
At times the connection between GoFlex and mobile drops.
How is your phone connected to the GoFlex? I don't mean for you to repeat that they are connected to the same hub. I mean, your phone doesn't appear to use iOS or Android as it's operating system, so you wouldn't have the GoFlex App running that allows your phone to connect to the storage device directly... or do you? I'm just curious as to what is actually informing you that the connection between the GoFlex and the phone dropped.
Now... it might be a POWER issue. The phone could be drawing/demanding all of the power that the USB port of the computer puts out, so by also using that USB flash drive in the same hub, and thus drawing power from the same port, you might be taxing the port. You could test this by removing the USB flash drive from the hub and seeing if it improves the situation. Normally, Windows would notify you if something like this was occurring, but the power issue could be right there on the edge of what would be tripped by the port itself. It could be inconsistent and still be a power issue, because not all the devices on the hub are drawing power AT THE SAME TIME. Again, you can test that by using the phone by itself on the hub for a while... or even by accessing the flash drive and storage drive at the same time (maybe copying some large files from one to the other) and seeing how the phone reacts.
It might be a cable length issue. I don't know how long the cable is from the computer to the hub, but that is tacked on to the total length to the phone itself.
It might be a combination of the ports of the hub AND the cable to the phone. Do you have another USB cable that you can try with the phone? I'm not saying that the ports in the hub are bad per se, and I'm not saying that the cable is bad, but the combination of the two... well, I've seen stranger things.
But honestly, when you remove the hub from the equation, and the phone works like it should... that tells me that maybe you should, you know, not use the hub for connecting the phone.