So my thought is that whenever Xur puts something in his inventory it is "blacked out" the following week. Meaning it will not so up the next week.
For example Xur is selling Voidfang this week. According to the black out system Voidfang would be blacked out meaning that Xur would have to pick one of the remaining 5 items the following week.
This system would only affect the item of the previous week meaning that the item that is blacked out would be refreshed the following week.
This could solve Xur bringing back items for multiple weeks in a row.
Edit: it may be better to have the "black out" to work on an item for a total of two weeks instead. That way you don't have: Voidfang, Sunbreaker, Voidfang, Sunbreaker, etc...
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It shouldn't be a "blackout" for one week, it should be for 2 weeks to prevent a rotating cycle of him selling one item then ell another then back to the first (like someone jokingly stated below).