I was doing some more research and captured the query that the MTA is periodically running to get the data.
One of the critical part of the SQL is the iState IN (51,55,61,62,71,81) If I compare these integer with the deliveryState enum the values are as (Start Pending, In Process, Retry Pending, Retry In Process, Pause Requested, Stop Requested). None of these values look promising from the point of view of my error. I checked the DB and the status of the deliveries in stuck stage is 15 (Target Ready)
SELECT iDeliveryId, iState, sLabel, iPriority, tsBroadStart, tsValidity, iDeliveryMode,sIPAffinity
FROM NmsDelivery
WHERE iDeliveryMode=1
AND iState IN (51,55,61,62,71,81)
AND iDeleteStatus=0 AND iIsModel=0 AND sIPAffinity IN ('default')
AND
(
iState IN (55,62,71,81)
OR (iState = 61 AND (tsNextPass IS NULL OR tsNextPass <= SYSDATETIMEOFFSET()))
OR (iState = 51 AND (tsContact IS NULL OR tsContact <= SYSDATETIMEOFFSET()))
) ORDER BY iState