During the Domino server startup if server finds there is an issue with the admin4.nsf it will perform the consistency check. While it is performing the consistency check it will not start the adminp task on the server however it will shutdown administration process task as shown below.
[0A68: 000C-1A08] 2021/05/13 06:30:23 Check the integrity of admin4.nsf ...
[0F28:0002-1380] 2021/05/18 06:30:23 Admin Process: Path: admin4.nsf: This database cannot be opened because a consistency check of it is in progress.
[0F28:0002-1380] 2021/05/18 06:30:23 Administration Process shutdown
Now if the server is not being monitored for the task then, your administration requests will not be processed on the server until the next Domino restart or manually loading the adminp on the server using the command "Load Adminp".
Needs an enhancement to start the Administration Process automatically after server completes consistency check on the admin4.nsf.