Asking for a mental health clearance letter at time of registration seems sketchy if the letter was already provided at time of permit application.
For state residents, the process is clear. You show your handgun training affidavit each time you apply for a permit to acquire. If you have a mental health clearance letter, you also show it to them when applying for either a handgun or long gun permit. Once the background check is done and the permit is issued, you've completed all the hoops you should have to jump through.
When registering a gun you acquired under a properly issued permit, there should be no need to produce anything related to the background check. Asking for a clearance letter at that point indicates that either someone is uninformed, or someone may have changed the policy to once again make things more difficult.
If someone is registering a firearm from out of state, that's different. HPD will collect some background info as if it were a permit application since the owner did not acquire the weapons under a HI-issued permit.
Since you have a long gun PTA, they should not be treating you like this is an out-of-state registration.
If EEF is right (no evidence to support his "guess"), they should be professional enough to give that reason when asking for the letter again.