Postgres 11

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CREATE TABLE

INSERT 0 19

SELECT subjectid, start_at, next_end_at - start_at AS duration
FROM  (
   SELECT *
        , lead(end_at) OVER (PARTITION BY subjectid ORDER BY start_at) AS next_end_at
   FROM  (
      SELECT subjectid, grp, big
           , min(ts) AS start_at
           , max(ts) FILTER (WHERE big AND big_rn = 2) AS end_at  -- 2nd timestamp
      FROM  (
         SELECT subjectid, ts, grp, big
              , row_number() OVER (PARTITION BY subjectid, grp, big ORDER BY ts) AS big_rn
         FROM  (
            SELECT subjectid, ts
                 , row_number() OVER (PARTITION BY subjectid ORDER BY ts)
                 - row_number() OVER (PARTITION BY subjectid, (value > 60) ORDER BY ts) AS grp
                 , (value > 60) AS big
            FROM   tbl
            ) sub1
         ) sub2
      GROUP  BY subjectid, grp, big
      ) sub3
   ) sub4
WHERE  NOT big                 -- identifies block of values <= 60 ...
AND    next_end_at IS NOT NULL -- ...followed by at least 2 values > 60
ORDER  BY subjectid, start_at;

subjectid	start_at	duration
1	2142-04-30 03:00:00	05:00:00
2	2142-05-04 03:30:00	03:30:00
2	2142-05-04 09:00:00	03:00:00

SELECT 3