The Mishnah Berurah in OC 188:6:16 - קפח,ו,טז says that if someone said Birkhas Hamazon on Shabbos and he is not sure whether he said Retzai or not, he must repeat the Birkhas Hamazon because we assume that [since he is usually not used to saying Retzai in Birkhas Hamazon] he must have not said it.
What if someone never eats bread during the week, only on Shabbos, and he is not sure whether he said Retzai or not, does he repeat Birkhas Hamazon?
The reason why one might have to repeat Birkhas Hamazon even in an a case like this, is (A) Maybe the halacha is univeral, (לא פלוג) - since most people do bentch sometimes during the week also, and they do not say retzai, and thus have to repeat when in doubt on shabbos, there is no personal halacha for those few who only eat bread on shabbos. (I'm not well enough versed in the rules of when we do or don't say לא פלוג.
Maybe since the "standard" version of Bentching is without retzai, we assume that everyone who bentches without paying attention, presumably said the standard version. And thus even if this specific persons always bentches with retzai because he only bentches on Shabbos, if indeed he did not recall saying it we would still assume that he said "the standard version without retzai. Is the reasoning why one must usually repeat because "HE" is used to bentching without Retzai, or because the standard bentching is w/o retzai, and we assume that he said the standard one.
NOTE: The Mishna B'rurah cited just says "אם ספק לו אם הזכיר או לא תלינן דמסתמא בודאי לא הזכיר: If he is not sure whether if he said [רצה] or not, without knowing otherwise we assume that he definately did not say [רצה]". He does not say why we assume so. The added explanation about being used to bentching without retzai, is my own understanding of his words, (thus the brackets).