In Eclipse Web, there are some exceptions that will allow you to edit a visual search in an advanced search:
All of one type of operator 1 or 2 or 3 or 4
Any number of and operators ending with 1 not operator 1 and 2 and 3 not 4
Any number of or operators ending with any number of and operators ( 1 or 2 or 3 and 4 and 5)
Any thing starting with or and ending with all ands then a not (1 or 2 or 3 and 4 and 5 not 6)
Any search referencing a saved search that meets the above criteria BETWEEN searches

If you receive the following error message, then there is something within the search criteria that will not convert.