§7 on the Protected Period says
Notwithstanding the above, no listing commission shall be paid to
Broker if this Agreement has either expired or been terminated upon
the mutual, written consent of Broker and Seller and the Property is
sold or contracted to be sold to a prospective buyer by or through
another licensed broker with whom Seller has signed an exclusive right
to sell listing agreement.
If you owe the Broker a commission, you owe it even if the agreement has expired, for example if the agreement expires before the closing, which is what the survival clause says (the end of the agreement does not mean the end of the broker's right to a commission, or the seller's obligation to pay). By putting this clause in, they explicitly say what common sense tells you – when you owe for a service, you have to pay even if the paying comes after the end of the agreement
So their rights are indeed indefinite, but if the agreement expires and is not renewed, they do not gain a right to a commission. §7 is the agreement-expiration escape clause.