some kind of interference issue when a radio stops transmitting on it.
So a radio stops transmitting and the repeater hangs on for a time with a weird static noise that sounds like it's being sucked down a bathtub drain. Correct? This is a classic example of IMD. An image of your transmit signal is showing up on your receive frequency and it retains enough of the PL/DPL component to keep the receive open and the repeater active.The interference sounds like squelch but coming through a tube..
So where could the problem lie? Anywhere in the antenna system and beyond. Suspect any component that is not PIM rated. Duplexer, connectors, coax (beware LMR users), antenna (not a fan of Diamond/Comet for duplex service), Also site environment. Rusty bolts, dissimilar metal contact, active equipment without proper filtering and on and on.
You can try and sniff around with a a good spectrum analyzer with high dynamic range or some receiver with heavy pass filtering so you can weed out the lowest of signals floating back to your receiver. Barring that you have a slog ahead as you swap out components looking for a change. A dummy load is a worthy troubleshooting aid in cases loke this.