Arabic term (edited): سقوط حق الخصم الذي

In the context, the noun سقوط really means إسقاط. The court will remove a right that had been previously established.

To revoke, abrogate, or rescind is to do away with a right, a law, or and agreement (to end the validity of something that was previously valid,

To forfeit something is to lose it by giving it up or relinquishing it, mostly by failure to do something that was essential for having it in the first place. In this case, however, it is the court that is removing the right, in case it finds the justifications presented unacceptable.

To lapse is simply to expire due to the passage of time.

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Note added at 12 hrs (2020-05-13 19:12:31 GMT)
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Answer to the asker's note:

Can we use the verb "forfeit" here?

My point is that the verb "forfeit" is used when the subject is the person who is losing the right due to his action or inaction. For example, if I am a boxer and I stop in the middle of a match, I will forfeit the match. I lose by forfeiture. What I am trying to say is that it depends on how you construct the sentence. You can say, "the opponent will forfeit his right," or you can say, "the court will revoke the opponent's right." The difference is on which subject you choose. In the source, it is the court. If you choose to reconstruct the sentence, then you will have to use "forfeit." I hope this is clear.

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Note added at 12 hrs (2020-05-13 19:35:50 GMT)
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If you like "forfeit" (which has merits) but you still want to be faithful to the source, you may want to consider using the noun form, "forfeiture." For example, you can say, "the court will decide the forfeiture of the right of the opponent who failed to pay . . . etc." The main point is that the forfeiture must be understood as the opponent's own doing. The court is not forfeiting. It is simply deciding that the opponent has forfeited. So long as you structure the sentence in this way, it should be fine.

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Note added at 12 hrs (2020-05-13 19:57:27 GMT)
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As you can see from the examples that I have given you, the choice depends on subtle differences that can be clarified or obscured as you build your sentence. "Lapse" is another choice that also depends on the meaning intended and on how you build your sentence. Consider the following:

The statement refers to the opponent having failed to pay. Was there a deadline for the payment? From the statement, we know that there was a previous decision to appoint an expert, and we know that the opponent had a right to uphold that decision. The statement wants the court to remove that right because the opponent failed to make a payment. Are they saying that the right was simply lost because the time to make the payment has lapsed? If time is of the essence in this case, then you can, if you choose to, say that the court should decide "the lapse of the right of the opponent who failed to pay . . . etc.). In this case, the passage of time takes center stage: the right dropped by the simple turning of the clock and the failure to pay within the time specified.

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Note added at 13 hrs (2020-05-13 20:18:01 GMT)
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In summary, here are the three choices:

1. The court revokes the right: The court makes a decision to remove the right (for whatever reason).

2. The opponent forfeited his right: He abandoned his right by failing to pay.

3. The opponent's right has lapsed: The opponent had a right, but the time to exercise that right has lapsed because the time to make the required payment has lapsed.