What is the effect of Talaaq Raj'i? After reconciling with the wife, does this Talaaq fall away?

Answer

If a husband gives his wife one Sareeh Talaaq (i.e. a Talaaq in which the word Talaaq/Divorce is used), then he may take her back without Nikah. However this one Talaaq will remain suspended for all time. It does not fall away. The husband will have the right to issue two more Talaaqs. Should he issue two Talaaqs in future in any way whatsoever, either together or separately, then the two together with the one already given will irrevocably and finally terminate the Nikah.

If he does not take her back before expiry of her Iddat (a period of three haidhs), then if they wish to reconcile, a fresh Nikah has to be performed. She will also be free to marry anyone else after expiry of the iddat.