See this answer: How to check internet access on Android? InetAddress never times out
However I would like to point out something that you may have overlooked: checking for constant internet connectivity will consume power. A lot of power. So, what you may end up doing is draining your user's batteries (which would have a lot of negative consequences, not just poor reviews).
So, maybe we could talk about why you need to check for internet connectivity constantly? You might want to look into how you can buffer up your network requests or caching ,etc. Feel free to edit this question or even create a new one, just link to it :)