Short answer: Yes, it will auto-stop, but not the moment your margin runs low. It only triggers after 5 consecutive failed copy trades. Before that, you will experience several failed copy trades until the 5th failure finally kicks you out of the system.

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What the rules say
There is a key line in Binance's official copy trading rules: When the margin balance of a copy trading project falls below the project's minimum copy amount, and there are five consecutive failed copy order openings, the project will be automatically closed.
In other words, the system gives you 5 chances. Each time a copy trade fails, your project still exists, but the copy trades keep failing. After the 5th failure, the system checks once a day and closes such projects.
What happens when margin is insufficient
It happens in two stages:
Stage one: Occasionally insufficient (fewer than 5 failures)
Your account margin is not enough, so when the trader opens a position, your copy trade fails directly and you miss that trade. The system returns an error message. The most common reasons are "insufficient margin" or "order amount is less than the minimum opening amount".
But the project still exists. You can continue copying the next trade. You just missed the previous one.
Stage two: After 5 consecutive failures
The project is automatically closed. You need to create a new copy trading project, choose a trader again, and start over.
Why your margin may be "insufficient"
Besides actually having too little money, there are two common situations that can cause copy trades to fail even when you still have funds:
The trader opens positions or adds margin frequently: If you use the "fixed amount" mode and the trader holds multiple positions at the same time or adds positions frequently, your account balance may not be enough to cover all the margin requirements for copy trading, causing later orders to fail.
The trader adjusts leverage: If you choose to "follow the lead trader's leverage multiplier", the system will fail your copy trade when it detects that your leverage does not match the trader's leverage.

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How to avoid this
Case A: Margin is almost gone, but you want to keep the project
Add funds to your futures account. You do not need to recreate the copy trading project. Once the balance is restored, subsequent copy trades will continue automatically.
Adjust the copy mode. Switch between "fixed amount" and "fixed ratio", lower the amount per copy trade, and reduce the margin requirement for each order.
Case B: You already have several consecutive failures
Go to the copy trading page and check the number of "recent failed orders". If you already have 3-4 failures, add funds or lower the amount immediately. Otherwise the next failure may directly trigger auto-stop.
Risk reminder: After the project is automatically closed, what happens to the positions created by your previous copy trades? Binance's rules do not clearly state how open positions are handled when a project is closed. It is recommended that you actively monitor your position status when margin is insufficient to avoid forced liquidation after the project is closed.
How to verify the fix worked: In the "order history" of your copy trading project, check the status of recent copy trades. If you see repeated "failed (insufficient margin)" entries, auto-stop is not far away. After adding margin, the next copy trade should show "filled", which means the project is back to normal.


