jsimons:
The terms you are inquiring about will be contained in the "Broker's Fees" section of the standard listing contract that the seller had with the listing broker. In the standard form it is a fill-in-the-blank item. (It wouldn't surprise me if they routinely write in a time frame such as 120 or 180 days.)
Here is a link to a sample listing contract - the applicable language is at lines 25-30: http://www.elkhartcountylistings.com/Listing%20Contract.pdf
The fact that an agent first showed you the property will be to the broker's favor, and they do watch to see what happens during that protected period after their listing expires. If their work brought the eventual buyer to the property, the theory is that they did their job and that they have earned a commission.
Ask the seller to check their listing contact. It should be pretty straight forward.
Let me know if you have any follow-up questions. If not, please remember to click on the ACCEPT link so that I receive credit for working on this matter with you.
Thank you!
Dan