eBay cases will time out after 30 days. I personally don't like letting them get to the point where the buyer has the opportunity to escalate, so will take action within the first 5 days whether the buyer is responsive or not, but I know sellers who never heard back from the buyer and let the case remain open without escalating themselves, and it ultimately just closed in their favour around 30 days later.

I don't know how clear eBay makes it these days to buyers that they're opening a refund request when they click "I didn't receive it", but I suspect a lot of the time the buyer sends that through, maybe or maybe not sees the sellers response (usually asking them to wait a bit longer), then the item arrives and they neither know or care to close or respond to a case. 

Some may be gaming the system, but many are just ignorant of and / or just don't care about what is happening on the seller's side in such situations, and are satisfied enough that their item arrived. I suspect sometimes emails go to the spam folder, as well. (Plus, far too many use throwaway or rarely used email addresses for online shopping - an absolute PITA when you actually need to communicate with someone).