Before getting into the details, it's important to note that Yala National Park is massive. It covers 979 sq kilometers altogether and is divided into five areas, commonly referred to as Blocks. Block 1 is the one with the most infrastructure and hence most thus popular with tourists. When people refer to Yala, they are usually referring to Block 1.
The government usually closes Block 1 for one month in September to do park maintenance.
However, there are other parts of Yala that are still very much open to wildlife enthusiasts. Most people head to either Block 5/Lumugamvehera for safaris and many people prefer that area of the park even when Block 1 is open as it’s less touristed and more wild.
An experienced guide is especially important when visiting these zones for a few reasons: 1) the animals outside of Block 1 are less used to vehicles and may be more challenging to spot. This will not be an issue for an excellent tracker. 2) the roads outside of Block 1 tend to be more rugged and require a driver with more skill and certainly a 4WD vehicle.
Happy Safari-ing, even in September ;)