Stopping Broadcast SSID on Sagem 2704N router

[#1]

PLuset directed me here.
I want to add my wifi to all specific devices.
I then want to stop broadcasting the wifi but still keep the existing devices which already have this wifi connected. Is this possible on this router please? In effect I don't want others to see my wifi broadcasting.
Plus net told me to uncheck the box next to broadcast SSID but it caused the wifi to stop broadcasting completely and dropped all the devices that were attached to it. I had to reconnect the router using the cable to reconnect the wifi to broadcast again and then reenter the passwords onto each of the devices again.
Many thanks for any help on this matter.

[#2]

Hi 'ASure, and welcome to the forum ! 

I have not used this Sagem 2704N, so can only give generic advice !

Firstly, the usual way of only allowing known wireless devices to connect to your WiFI, is to enable MAC address authentication.
Every wireless device interface will have a unique MAC address, which you add to an "allowed access" list within your wireless access point.
Only the devices on that "allowed list" will be able to connect to the WiFi, so it is irrelevant whether your SSID is visible or not.
Check to see whether your router's wireless settings allow a MAC address whitelist to be configured.

Secondly, hiding the SSID does not improve security.  Common WiFi hacking tools can quickly discover hidden SSIDs.
It is actually helpful to broadcast a meaningful SSID which identifies the WiFi signal as yours, because it can help your neighbours identify nearby wireless signals as yours, and therefore choose to set their WiFi channel number to something different from yours - thereby reducing channel interference with your WiFi signals and improving performance for both of you. 
If you want to improve security, then choose a really hard to crack WAP2 authentication password key !.

Quote from: ASure

uncheck the box next to broadcast SSID but it caused the wifi to stop broadcasting completely and dropped all the devices that were attached to it

Wow! that is really bad,I must have used maybe 30 different wireless routers and wireless access points, and have never seen that happen !

[#3]

Looking at the setup guide on the Help pages, it seems you may have unticked the wrong box: See here http://www.plus.net/support/broadband/hardware/plusnet-2704n-wireless.shtml

Setting
What does it do?

Wi-Fi Enabled (tick box) Switch Wi-Fi on or off note, this setting can also be controlled via the Wi-Fi button on the side of your router.
Wi-Fi Name (SSID) The broadcast name of your wireless network. This is what you'll see when scanning for networks to connect to.
Channel
Choose the channel (frequency) that your wireless network transmits on. By default this will be set to Auto.
• Auto means the your router will choose the best channel each time you switch it on
• Manual allows you to choose a single channel to broadcast on (between 1-13)
If you're having problems, using a single channel can improve the stability of your wireless connection.
You'll need to experiment to find the channel that's best for you. We recommend trying channels 1, 6 or 11 first. For more on this, please see our Wireless signal guide.