Hi,
There are some limited scheduling functions built into Auto-Relist that could keep a cycle of relist submissions rotating and might even help fill gaps for BIN sales to keep items constantly available. It does have a Weekly (day and time) relist function e.g. Sat 12:55 PM Relist works on the basis of listing close and choice of status at close: sold/unsold/partial sold, relist credit, and inventory available.
It may not be a perfect solution, but it's worth a look.
What duration are you using on those listings?
Danno