I had this problem. Nothing to do with the antenna - the Kindle WiFi antenna worked fine.
Turns out the Kindle Voyage, and other Kindles as well, can't cope with the way my (Virgin) router does dynamic allocation of network addresses in a password protected network.
The only solution I could find that worked was:
1. Set up an extra 'guest network' on your WiFi router. Call it something like 'our Kindle network'
2. On that network only, turn off the password protection
3. On that network only, in the router setup, turn on 'MAC Address Filtering' and choose the option that accepts (as opposed to blocks) the designated MAC Addresses.
4. Find the 'MAC Address' of the Kindle, in the Kindle Settings menu.
5. Type the MAC Address of the Kindle into the 'allowed MAC Addresses' list in the router.
6. Repeat if required for other devices.
This has worked perfectly. It remains secure because only the allowed devices (defined by the MAC Addresses stored in the router) are allowed on that network. All other devices are blocked. Your normal WiFi network(s) is(are) not affected and stay password protected as before.
(The MAC Address is a hardware identifier unique to each device, so you'll need to change it if you get a new Kindle.)