Idea Tab a2109a wont connect to wifi without ssid broadcast

Question

I have Idea Tab a2109a that connects to my wifi just fine, until i shut off the ssid broadcast from the router. At that point it stops connecting and says out of range. Laptops and a KindleFire have no problems maintaining a connection without the broadcast.
Running Android version 4.1.1
Kernel version 3.1.10
Model number IdeaTab A2109A
How do i maintain a connection on this tablet WITHOUT the ssid broadcast?

Answer 1

I tried your suggestions as much as I could at the corner coffee shop, but they didn't help.
I didn't follow them exactly because I misinterpreted turn WiFi on as turn it off. But when I sort of made up for that, I could not access it.
I realized my mistake when I came back home, went back to the coffee shop and tried again. Unfortunately, the signal was now one bar, and so I'm not sure that I've proved anything.
As I came back home, I searched for my network. I found it almost at my front door and with a strong signal. I walked around the outside and the access would come and go. Every time I could get access again it was always strong, even as neighbors' networks varied in signal strength. So, I couldn't double check if I would have gotten through with a weak signal.
So, I can access the web on my iPod touch on a closed network but not an open network.
I can access it at home with an ActionTec GT701-WG DSL modem. I can access it with a coffee shop provided access to ClearWire, a wireless Internet provider. This latter requires registration at hotspots.
I have software version 2.0.2 (5C1).