Well there are a few things that could be causing it.
The first thing I would suggest you do is restart your modem/router. Although, as you say, the other device works fine with it, that is no guarantee that any other device will. Tablets can be quite picky.
Second thing to do, after or while you restart the modem/router, also restart your tablet. However, make sure the tablet does not load first. It needs to finish restarting after the modem/router.
Third, if necessary, remove the data/info for your connection on the tablet and then re-add it.
Fourth, make sure you check, and if necessary adjust, the WiFi sleep policy on the tablet. It can often cause this.
To check to see if this is the issue...
1. On the home screen of your...