GROUP BY possible sequences
select      log_id
           ,array_agg (sequence)

from       (select      log_id 
                       ,sequence
                       ,count (is_restart) over
                        (
                            partition by    log_id 
                            order by        made_at
                        ) as restart_id

            from        (select      made_at
                                    ,log_id 
                                    ,sequence
                                    ,case 
                                         when sequence &lt;
                                              lag (sequence) over
                                              (
                                                  partition by    log_id 
                                                  order by        made_at
                                              ) 
                                         then 1
                                     end            is_restart

                         from        logs
                         ) l
            ) l

group by    log_id      
           ,restart_id

order by    log_id      
           ,restart_id
;


+--------+-----------+
| log_id | array_agg |
+--------+-----------+
| 206480 | {1,1,2,3} |
+--------+-----------+
| 206480 | {1,2,4,5} |
+--------+-----------+
| 206480 | {1,2}     |
+--------+-----------+
| 206481 | {1,2,3,4} |
+--------+-----------+


Walkthrough


Identify restarts by comparing current sequence to previous sequence (LAG).

select      made_at
           ,log_id 
           ,sequence

           ,case 
                when sequence &lt;
                     lag (sequence) over
                     (
                         partition by    log_id 
                         order by        made_at
                     ) 
                then 1
            end            is_restart

from        logs


+---------+--------+----------+------------+
| made_at | log_id | sequence | is_restart |
+---------+--------+----------+------------+
| 1       | 206480 | 1        |            |
+---------+--------+----------+------------+
| 2       | 206480 | 1        |            |
+---------+--------+----------+------------+
| 3       | 206480 | 2        |            |
+---------+--------+----------+------------+
| 4       | 206480 | 3        |            |
+---------+--------+----------+------------+
| 5       | 206480 | 1        | 1          |
+---------+--------+----------+------------+
| 6       | 206480 | 2        |            |
+---------+--------+----------+------------+
| 7       | 206480 | 4        |            |
+---------+--------+----------+------------+
| 8       | 206480 | 5        |            |
+---------+--------+----------+------------+
| 9       | 206480 | 1        | 1          |
+---------+--------+----------+------------+
| 10      | 206480 | 2        |            |
+---------+--------+----------+------------+
| 11      | 206481 | 1        |            |
+---------+--------+----------+------------+
| 12      | 206481 | 2        |            |
+---------+--------+----------+------------+
| 13      | 206481 | 3        |            |
+---------+--------+----------+------------+
| 14      | 206481 | 4        |            |
+---------+--------+----------+------------+

Do "running counts" (similar to "Running totals") of restarts (is_restart).
Rows that belongs to the same group will have the same count (AKA restart_id).
The "Order by" in COUNT implies range between unbounded preceding and current row 

select      log_id 
           ,sequence
           ,count (is_restart) over
            (
                partition by    log_id 
                order by        made_at
            ) as group_id

from        (...) l


+--------+----------+----------+
| log_id | sequence | group_id |
+--------+----------+----------+
| 206480 | 1        | 0        |
+--------+----------+----------+
| 206480 | 1        | 0        |
+--------+----------+----------+
| 206480 | 2        | 0        |
+--------+----------+----------+
| 206480 | 3        | 0        |
+--------+----------+----------+
| 206480 | 1        | 1        |
+--------+----------+----------+
| 206480 | 2        | 1        |
+--------+----------+----------+
| 206480 | 4        | 1        |
+--------+----------+----------+
| 206480 | 5        | 1        |
+--------+----------+----------+
| 206480 | 1        | 2        |
+--------+----------+----------+
| 206480 | 2        | 2        |
+--------+----------+----------+
| 206481 | 1        | 0        |
+--------+----------+----------+
| 206481 | 2        | 0        |
+--------+----------+----------+
| 206481 | 3        | 0        |
+--------+----------+----------+
| 206481 | 4        | 0        |
+--------+----------+----------+

Group by log_id and restart_id and aggregate sequence

select      log_id
           ,array_agg (sequence)

from       (...) l

group by    log_id      
           ,restart_id

order by    log_id      
           ,restart_id
;


+--------+-----------+
| log_id | array_agg |
+--------+-----------+
| 206480 | {1,1,2,3} |
+--------+-----------+
| 206480 | {1,2,4,5} |
+--------+-----------+
| 206480 | {1,2}     |
+--------+-----------+
| 206481 | {1,2,3,4} |
+--------+-----------+