Try to identify if you have a ground that switches to power/enable your relay.
Meaning - instead of a power source going to your relay to power it, another relay controls the ground [-neg/0V] to activate the relay. Power already present at that specific relay waiting on a [-neg/0V] source to activate.
In my set-up on the the interact I had a relay that switched [fluttered] like you stated and it was controlled by a [-neg/0V] switching relay, I found a bad [-neg/0V] wire. It rang out fine, but could not handle any significant load.
Is this all your relays doing this? Or is it a section that controls a specific area?
Can you try to disable/disconnect relays in the series [assuming the problematic ones are in a series] to identify if one is failing causing a cascading effect. I know electrical gremlins are difficult to track down.
If you want give me a call and I can try to give you hand in troubleshooting.