what would happen if before site goes "offline", we still have open session waiting for deposit
and the bitcoin deposit got stuck in limbo because very low tx fee was used
then we couldn't extend it when site goes "offline" for a few days
can we recover it by proof of signature from sender address or something?

If you have a limited access to our service, please contact support. We can either extend your session (if your deposit is still pending) or issue a voucher you can use anytime you want.