If you are not the original owner, then Fluke, technically, has no obligation to fix it under warranty for you.
Here are the options that I see.
1) If the date and time setting are not required, just ignore the problem and leave the capacitor as is. Alternatively, you can remove the capacitor and the unit will function fine. Note, I can't remember if it is in this thread or this model, but at least one person who removed the capacitor couldn't get the meter to power on again. So there is a non zero chance of screwing something up if you are not careful (lift a solder pad, short something out, zap components/pcb with ESD, etc).
2) Fluke built its service reputation in the past, as reported here and in other forums, by providing fantastic service to the customer. Sometimes, but not all, the service centre will fix the problem regardless of the terms and condition of the warranty for free.
So you could take a chance and send it to Fluke (make sure you get a tracking number + insurance) for around $10 USD and see if Fluke will fix it under warranty and ignore the fact that you bought it from ebay second hand. It is my understanding, and you should confirm by talking to a customer service representative, that if you do not qualify for warranty repair that Fluke will contact you with an $$ estimate to fix your meter. Then you can decide if the price is reasonable or not. If you choose not to get it fixed due to cost, then Fluke will send it back to you unrepaired. I believe Fluke will pay return shipping so at most you are out the original shipping costs.
Again, you may want to talk and verify with a Fluke customer service representative. If you choose the second option, please report back so we know the outcome.
PS. I am well aware of negative posts about Fluke customer service. I find that by talking nicely to a person and treat them the way you expect to be treated, that you will get a lot better result.