I celebrate and list the next one the next week, and usually get no bids on it. I'm just a small time seller with too little time to be strategic, but for the people who do this for a living I could definitely see them offering second chances.
I've never responded to second chance offers...usually because I was outbid in the first place and that was my max amount. I've also received second chance offers from scammers, so be careful there too. I report them to ebay first thing.
Another danger is hacked accounts. I have received second chance offers on Ebay before and the email offering it was hacked to look like Ebay but it was thieves who hacked the information and were trying to steal. ALWAYS verify again through Ebay if the seller offered you a second chance. If there is a phone number listed call it. I was considering sending out $2200 once but stopped and called and found out there was never a second chance offered to me. Chris