X1 is set to carry over search terms, by default, only when you hold down the Shift key and then click the new search tab. For example, if you are on the Inbox search tab and have already entered your search, hold down the Shift key and click the Email search tab. This will transfer your search criteria to the new tab.
If, however, you want to always carry over your search term when switching search tabs (i.e. without having to hold down the Shift key), access the Tools > Options > Searching menu. In the Search Term Carry Oversection, click the drop-down and change the option from Shift to 'Blank' and click OK to save your change