The extension is nearly guaranteed. In the 30 years I have been here I have only "heard" of one instance of a person being denied, and I am skeptical of the source of that information.
As long as you are honest and DON'T break any laws, like overstaying your visa, you should have no issues.
But remember the fine print with Immigration in any country, the final decision is up to the Immigration officer. Hopefully they are not having a bad day or you pissed them off for reason.
Jamaica relies on tourism for much of its GDP, so it in their benefit to extend an existing visa. You will be spending more money on the island!