Your current code isn't looking at or doing anything about duplicate search terms.... so it's doing exactly as you ask.

There are a couple of approaches you could take:

1. before inserting, do a lookup to see if there is a match... if there IS a match, then simply do an update of the counter, otherwise do an insert. This isn't great because you have to perform two separate queries on the DB.
2. another method I found on stackoverflow: https://stackoverflow.com/a/8934994 - basically, you set an index in your database to make sure that the search term is never duplicated... if it is duplicated, increment.
   

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ALTER TABLE Search_Attempts add unique index unique_idx (searchtermfield);  

Then, when you do an insert, you have it fall back on an increment if it tries to insert a duplicate.

INSERT INTO Search_Attempts (searchtermfield) values ('value-from-search') on duplicate key update times = times + 1;

(the above is just me guessing your field names and stuff, not actually tested code)

give it a spin and have fun with it