The biggest problem with the Batista regime, as I understand it, is that the people running the show had little to no competency in their roles. It wasn't just that they were corrupt, but they were incapable as well. This is particularly true of the armed forces under Batista, and is part of the reason that his regime collapsed so quickly; many of the officers fighting Fidel Castro and his revolutionaries just didn't know what they were doing.
There's also the fact that Batista's regime lacked any real ideology of any sort. The goal of his government, plain and simple, was to generate wealth. Primarily for himself and those bankers at the top, but also with the belief that enough wealth generation could assuage the masses. In keeping with this, Batista actually allowed a reasonable amount of opposition to operate in the public sphere (though obviously not armed) in hopes of making himself look more benevolent both to the people and to the US government, which increasingly (and accurately) saw him as a liability. This undermined him severely, and again, is part of why his government collapsed as quickly as it did.
With these factors in mind, I don't see Batista lasting much longer than he did IOTL. There were a number of attempted coups within his government before Castro et al ever marched on Havana, and he would've been taken out sooner rather than later. As to who would've/could've taken him out successfully, i'm not sure, and whether or not they would run an equally incompetent government will determine if a different revolutionary group could overthrow them.
This (Chapter 5 specifically, beginning on page 113) is a good look at the things I outlined here briefly.
https://books.google.com/books?id=rPNSnRYzIdgC&pg=PA118&lpg=PA118&dq=batista+regime+sultan&source=bl&ots=jfhJsAbs8S&sig=XyQPTBcXsx46SJTn4UF2Clap5ZY&hl=en&sa=X&ved=2ahUKEwiI5vK74qLeAhVJ1oMKHe5gCokQ6AEwDHoECAYQAQ#v=onepage&q&f=false