First, let's take a look at your query:

WITH date AS
(SELECT ID, 
MIN(time) AS minDate, 
MAX(time) AS maxDate
FROM tablename
GROUP BY ID)
DELETE FROM tablename
  WHERE 
    NOT EXISTS 
      (SELECT 1 FROM tablename
        WHERE tablename.ID = d.ID 
          AND tablename.time IN (d.minDate, d.maxDate));

Let's state what this means with plain words:

"Let's get the ID, minDate and maxDate for each ID group from tablename and then, using this result, let's remove all records whose ID matches one of the group, but whose time differs both minDate and maxDate"

The flaw in the logic is that your intended query would translate to this:

"Let's get the ID, minDate and maxDate for each ID group from tablename and then, using this result, let's remove all records whose ID matches one of the group, but whose time is outside of the range of minDate and maxDate"

So, let's change the operand of the IN known for set theory to ranges:

WITH date AS
(SELECT ID, 
MIN(time) AS minDate, 
MAX(time) AS maxDate
FROM tablename
GROUP BY ID)
DELETE FROM tablename
  WHERE 
    NOT EXISTS 
      (SELECT 1 FROM tablename
        WHERE tablename.ID = d.ID 
          AND NOT (tablename.time BETWEEN d.minDate AND d.maxDate));

or, if you really like mathematical symbols, then

WITH date AS
(SELECT ID, 
MIN(time) AS minDate, 
MAX(time) AS maxDate
FROM tablename
GROUP BY ID)
DELETE FROM tablename
  WHERE 
    NOT EXISTS 
      (SELECT 1 FROM tablename
        WHERE tablename.ID = d.ID 
          AND NOT (tablename.time >= d.minDate AND tablename.time d.maxDate));

But it seems that the query fix by itself will not solve your problem. You have data in different formats in your example, which means that you store the date as text. You will need to fix your data as well, make sure you have a date/time field rather than a text field or, if you really really need (?!) or prefer them to be stored as a string, then make sure that they are converted for the purpose of the comparison into a format which alphabetically would yield the same order as logically for the dates.

EDIT

Your date/time information is also separated into two separate fields. My query assumes this information to be part of a single column. If you have two columns, then you can concatenate them, but really, you should unite them into a single field (that's actually a criteria for 1NF as well) and convert it to date/time.