Remove them after each trip. Otherwise you're going to risk corrosion to the crown at the very least, and maybe the barrel too (especially if you store your rifles muzzle up).
When I'm not shooting, the suppressor is off the rifle, in the rifle case. If the rifles are in the safe, the suppressor is on a shelf in the safe. Mine are direct thread. Easy enough to spin them on and off.
For storage I leave it on a rifle. If I store it separately Im prone to forget/overlook it on the next trip out.
I do loosen or remove it after each shooting session just to avoid the possibility of carbon locking it up but I put it back on once its all cooled back down.
My Omega stays off unless I'm shooting. The rifle(s) with the Omega attached are long enough that sure as hell, I'd bash the can up against something, tweaking it out of alignment and I'd get a baffle strike. I had the Quick-Detach ASR Mount(s), but I didn't really like them. Seemed too finicky for my tastes. I certainly liked the muzzle brake function though. I was a bit surprised because I thought I'd like the ASR concept better than I did. I really do like direct thread and I'm finding I have to screw around with the can less. Not sure about anyone else but I use a little bit of NAPA copper based Anti-Seize compound on the barrel threads. A little bit goes a long ways and helps to prevent stainless on stainless galling and seizing. Ask me how I learned that lesson......
DT Omega with a little copper based anti seize. Loosen while it's still hot after shooting, tighten it once its cooled down again. Clean it every couple of trips, rinse and repeat.
I leave it on unless I take my baja bug out shooting. Doesn't 28" barrel + can doesn't fit so well in the little bug. I'll swap it between rifles occasionally but it's usually on the 6.5 SAUM. Clean every 200 rounds or so to keep it from getting stupid hard to take apart.
I take my suppressor on and off constantly between 3 different rifles. Never have a POI shift once zeroed with the can on each one. Just make sure it stays tight when shooting.
Guess I'm the odd ball here. I take it off when I clean. Other than that it's always on. Direct thread. Use anti seize on the threads when I do clean and reassemble. I don't clean often either, so it stays on for hundreds of rounds at a time typically.
Mine comes off when after each range trip and then it goes right back on. I've had suppressors get stuck before so removing them and anti seizing the threads helps. Rifles are stored with the suppressors on and I've never cleaned a can.