Which version of 8.2 are you on?
Were the alerts you have acknowledged created on the server where you are trying to delete them? Or are you deleting them from a central manager?
I have tested this on V22.214.171.124 and v126.96.36.199.1 and I do not have this issue. I can acknowledge alerts and then delete them without having to acknowledge them first.
I hope to have some of my test servers upgraded to 188.8.131.52 later today or tomorrow and will test it on that version too.
We're on 184.108.40.206. A bit of extra info, the user activity log seems to think my deletes are successful:
System Fault Deletion Success Deleted system fault types "Link failure of Port: 11A, Link failure of Port: 11B".
It's a known issue, resolved at manager hotfix version 220.127.116.11.1. As hotfixes are only available from support (this should exist in the next public MR release as well), open a support ticket or call into the support queue, and mention this bug # to get a copy of the hotfix:
1098216 Unable to delete acknowledged faults in the System Faults page.