I have seen this problem with other Android tablets. It appears to somewhat version dependent. I don't know that there is one cause or solution, but here are a few ideas that may help. Tell the tablet to forget the current connection and try these.
Change the WiFi channel on the router and retry. Set the channel specifically to 1, 6, or 11. Try each one.
Rename the SSID and retry. If you get a connection change the SSID back and retry.
Make note of the encryption password then temporarily turn off encryption. Try the encrypted connection with the tablet. If it works,and reset the encryption, using WPA2 if possible or WPA.
Please post back with the result and note what worked or didn't work for you.