No. Nothing requires you to go live, on a schedule or at all. Plenty of stores sell entirely through listings. Can I sell without going live?
There is no penalty for a quiet month and no ranking that punishes you for it.
What a rhythm actually buys
A reason for a follower to come back. A follower is only worth anything if there is something to return to. "Thursdays at 8" is a thing people can remember; "sometimes" is not.
Compounding instead of starting over. A store that goes live at random starts each show from zero. One with a slot accumulates a room.
Your own learning. Four shows a month teaches you what sells; four shows a year teaches you almost nothing, because too much changed in between.
The honest cost
It is a commitment to a specific hour, and a missed one is worse than a slot you never claimed — people who turned up and found nothing do not turn up twice.
So pick something you can actually keep. Once a fortnight, kept, beats weekly, missed. That is the whole of the advice.
If you are starting
Do not announce a schedule. Run three or four shows at times that suit you, look at what the numbers say, then claim a slot.
Your analytics has a Timing tab built from your own buyers rather than a general rule, and shifting a show by two hours is free and is usually the highest-return change a small store can make. How to find your store's numbers
What matters more than frequency
Sell-through. A show where most of the lineup sells is worth more than three where little does, and a bigger audience does not fix a lineup or pricing problem. What is sell-through?
The first minute. Most of the people who leave a show leave early, because nothing is happening yet. How to go live
Having something to show. A show run because it is Thursday, with nothing good in it, costs you more than skipping it.
If you stop
Nothing is taken away. The room gets quieter, which is recoverable in a few shows. What happens if I stop selling for a while?
The middle path most stores land on
A scheduled show when there is enough stock to fill one, announced to followers a few days ahead, plus ordinary listings running the whole time. The listings sell while you sleep; the shows bring people who then follow you. How to schedule a show
More: how many items should a show have, what is sell-through, where do I see how my show did.