So a buyer recently bought an item of mine nine days ago

 I won't delve into the issue that the buyer had with the product, but what I will say is that they opened a case on the 19th, requesting a refund and to return the item. We communicated back and forth with eBay messages and in the end, the buyer decided that she wanted to keep the item and to "move forward". I told them that since wishing to move forward, then the right thing to do would be to close the case. This was from an email sent yesterday night.

Here's the thing: we the seller need to respond to the case by tomorrow. If I were to respond to the case, it means we must comply with the buyer's preference, which is a full refund. The buyer has not responded to my email yet nor has made an indication that the case will be closed. She's a very new buyer to eBay as well - the day she bought the item was the day she joined eBay! I honestly don't know what to do now: I either comply with the refund and lose the money, or I ignore the case, in which Customer Service takes over and forces out a refund. No matter what, I will be losing money because the buyer has not taken any visible action.

The only thing I have to hope now is that the buyer already did took action and to play the waiting game - I believe that there's a 7 day waiting period or am I mixing up some facts? I will be contacting the buyer again tonight. Any suggestions or ideas what to do at this point in time?

did you respond within the case to return for refund? if so buyer has to return with tracking within I think 7-10 days. if they don't return within the required time with viewable tracking the case will close in your favor. don't close it yourself, it will close after 30 days