From my experience, second chance offers are rarely accepted.  Not sure if it's because the other bidders have lost interest, already moved onto another listing or because they are not quite trusting of a transaction that has fallen through (even if its not the seller's fault).   Other sellers might be quite successful with second chance offers though...

I think the wording "relisted due to non-payment. My apologies for any inconvenience to other bidders."  is a good way to word things, especially with the second sentence. It explains the situation but also says something about the seller being polite and serious about selling.  

But as for payment time, I ask for payment within 5 days, and like other posters here suggest giving them a week/  I also give 2 friendly reminders along the way and inquiries as to whether everything is OK before telling them "Unfortunately if I don't receive communication by ___ date I will have to open an unpaid item dispute".  This tells them you're not keen on escalating it but they will be forcing your hand.