Detailed Explanation

To answer "Matchmaker, Matchmaker", it is important for us to:

A) Identify the basis of the time-honored custom to remunerate matchmakers for their work

B) Configure the value of the service Mrs. Hellman may have provided

C) Quantify the termination of the matchmaker's service.

• A. Identification:
  

Typically, a matchmaker brings the bride and groom together by
1) The respective parties requesting the matchmaker's services, or
2) The matchmaker suggesting a prospective match and offering to render his or her services.
 
Thus, a matchmaker, [Choshen Mishpat 185: 6, Pischei Teshuva, 185:10] like any broker [Biur HaGra ibid. 13] or sales agent, can provide one of two categories of service:

1) Solicited work, or
2) Unsolicited work

We have noted in previous issues [See Issues 14, 19, 29, The Case of the Baffled Babysitter- Special Edition, 39] that one is generally required to pay for receiving benefit from an unsolicited service that he or she would otherwise have willingly paid a third party to perform.[Choshen Mishpat 375:1 (Note: See Issue 40 for a list of exceptions)]

To this date, people willingly hire matchmakers to assist them in their quest; consequently, the bride and groom must remunerate a matchmaker who initiated his or her services, just as they would owe anyone who provided them unsolicited work for which they would have been willing to pay.
 
The amount due for receiving matchmaking services is, like all employment rates, subjective to the custom of the local society [Choshen Mishpat 333:1].
 
• B. Configuration:

Like a real estate agent, the job of a matchmaker can be multifaceted:
1) To introduce the parties
2) To aid in negotiations
3) To ensure the prospective relationship materializes [Pischei Teshuva, 185: 10]

Should the relationship materialize, each facet performed, earns the matchmaker one third of the going rate [ibid.]. 
 
Again, the amount due for receiving matchmaking services is, like all employment rates, subjective to the custom of the local society [Choshen Mishpat 333:1].
 

• C. Quantification:

Undoubtedly, a matchmaker provides information, which could be of value later, whether or not he or she is involved in brokering and/or actualizing the relationship.
 
The question at hand is, "Are the prospective sides forever beholden to the initial information provider?"

The answer is one that demands a level of personal honesty.

If the prospective sides close the file, they owe nothing to the initial matchmaker even if they subsequently meet again.  If, however, they never fully closed the file, or else, the first encounter nevertheless enhances the second meeting, they owe the initial matchmaker his or her share for introducing them to each other.

A regulation of Prague, which became the accepted custom across the Jewish spectrum, was to award the initial matchmaker should the prospective sides have met again within the same year.
 
Within the same year, we can assume that the two parties consciously or subconsciously never really parted ways. Hence, the initial matchmaker deserves his or her due share.  However, once a year elapsed we can assume that both sides have parted ways seriously, and any subsequent relationship formed is independent of the initial matchmaker's efforts.

Nevertheless, as inferred above, if the prospective sides know within themselves that their original encounter enhanced their subsequent meeting, they would be responsible to their initial matchmaker even after a year has passed.

Application:

For all intensive purposes, Aaron and Leah forgot about each other after their first dating experience.  Three years passed until they chanced upon each other in the air. Objectively, Mrs. Hellman's services terminated with no success. They therefore must remunerate Mrs. Hellman only if their original encounter played a role in striking up serious conversation on the flight.  Should it have played a role, the Berger's would be liable to pay Mrs. Hellman 1/3 of the going matchmaker's rate, for having introduced them to each other.