AWS DMS Task getting failed after completion with error as AlwaysOn BACKUP-ed data is not available
I don't know if you're still working through this, but I wanted to post the problem &amp; solution for anyone else.
There is a bug in the AWS DMS replication engine version 3.4.3 when using RDS SQL Server as a source endpoint, where the 5 minute log backup used for point-in-time recovery with RDS disrupts the CDC process. The solution/workaround is to use a different replication engine version set on the replication instance, such as v3.4.2.
From AWS support:

Root Cause:
Researching internally, I observed this error to be a know issue with
DMS replication instance running the version 3.4.3,
where RDS SQL Server has truncated active transaction logs (TLOG) or
there are no activities in the database. This is a known situation
when using RDS SQL Server as a source.
Why task failed:
DMS 3.4.3 tasks are failing due to missing LSNs in source RDS SQL
Sever databases, when source SQL Server MS-CDC enabled tables remains
idle for a long period of time, the DMS task still fails even when you
increase the MS-CDC polling interval on source database.
This is because MS-CDC polling interval prevents TLOGs truncation only
when there are changes on source tables, if source tables remains
idle, the LSNs does not increment, then the RDS t-log backup job
removes the LSNs from the online t-log that are required by DMS,
causing this issue.
Additionally, DMS task is failing with misleading errors such as:
00016458: 2020-12-28T09:30:08 [SOURCE CAPTURE ]E: Failed to access LSN
'00001002:0001c389:0003' in the backup log sets since BACKUP/LOG-s are
not available. [1020465] (sqlserverendpoint_capture.c:717
This error can still occur even when MS-CDC Polling interval is set to
sufficient value, it happens when the RDS t-log backup job removes an
LSN from the online t-log. This issue is especially seen in databases
with less traffic since the LSNs are not incrementing and DMS is
looking at the last committed LSN.
Workaround:
I would recommend trying to migrate the same tables by creating a
similar task using DMS RI version 3.4.2 or 3.3.4