The address will not expire ever, but, depending on what will Binance do internally, it may be that they will no longer use nor watch the wallet(s) having the old addresses, hence the user accounts will not get funded if money will come to those addresses.
Technically, the address will not expire, but to a centralized exchange, it may. And that's what's happening right now. Binance is putting an expiration to addresses, although leaving users the opportunity to still get their money with a few more clicks. But Binance reserves the right to disable this function anytime. And I think this is not a matter of if but when. Binance will certainly not maintain this feature forever. And when that time comes, tickets and complaints are gonna be flooding Binance's support.
And what's more controversial in the coming months or years is when despite the warning, before finally disabling this "click to credit" function, that deposits to expired addresses should be avoided and any funds deposited to them may be permanently lost, these funds will move.