TL;DRWhen you approve, the token itself records that a spender may move up to a set amount of your balance. That record stays until you change it, no matter whether you ever open the app again. Reading it is free; changing it is one small transaction from your wallet.
The record lives in the token, not in the app
Exchanges, lending apps and marketplaces cannot pull tokens from your wallet on their own. Before they can, your wallet calls approve on the token contract and names a spender, usually the app's router or vault, and an amount. The token writes that pair into its own storage.
From then on the spender can call transferFrom and move up to that amount of your balance. The app's website, its servers, even whether the company still exists, have nothing to do with it. Only the token's record counts.
Why it stays open
Nothing expires an ERC-20 allowance. Some apps ask for exactly the amount of one trade, and the allowance drops back as it is used. Many ask for an unlimited amount so you never have to approve again. That second kind stays fully open for as long as the token exists.
Most of the time that is fine: a well-built router only moves tokens when you send it a trade. The risk is in what you cannot see. If a spender contract has a flaw, or the address was never the app you thought it was, an open allowance is what lets it act.
What you can do about it
First, look. Nullo reads the approvals your address gave on Robinhood Chain and shows the current amount, not an old event. Then decide per spender: keep the ones for apps you still use, close the ones you do not recognise or no longer need.
Closing means calling approve again with an amount of zero. It costs a little gas, and your wallet shows you the call before you sign. You can always approve again later if you return to the app.
Try it on your own address
Read your open permissions in a minute.