What would you think?

[Footface]

Buyer won item last Saturday. Heard noting from them. Tues I sent an invoice to remind them, Wednesday I opened as I'd heard nothing, this morning they emailed me asking me to close the case as they were hoping to win my other items which finish on Monday night. ( no apolopgy)
Would you block them and keep the case open

Or close case and hope for best.

Tbh I just want a quiet life!

I'd reply politely but say that the case will remain open until the other auctions close.

I would close the case and relist and block them too

If I close the case can I re list straight away?

yes - as long as it is 4 days or more since you opened it.