What is the ruling on a wife boycotting her husband for more than 20 days for flimsy reasons, despite the husband's admonition to her?

It is not clear from the question who is boycotting whom. However, if the husband is the one boycotting, he may boycott his wife if she is disobedient, based on the verse: "As for those [wives] from whom you fear defiance, admonish them; forsake them in bed" [An-Nisa: 34]. The Prophet, peace and blessings be upon him, boycotted his wives for a full month. But if there is no reason for the boycott, the husband should not boycott his wife, in accordance with the verse: "And live with them in kindness" [An-Nisa: 19]. If the boycott is from the wife, then refer to Fatwa number 47359.