My standard procedure when hunting is to hunt with a round in the chamber, safety on and as soon as the day is over or while getting into a vehicle to remove the bullet from the chamber.
This can happen a lot since it's not unusual to go several days without firing a shot, does chambering the round over and over again result in a loss of accuracy compared to a round that has only been chambered once?
If chambering a round deforms or otherwise mars the bullet, it may have a decrease in accuracy. Even a damaged case can change the point of impact for very long range shots. Also, accuracy is a relative term. Anything that varies the variables from those present when you shoot from your benchrest conditions will change the point of impact and therefore "accuracy".
If you are looking at "Minute of Elk" accuracy out too 300-400 yards (meaning good enough for shooting an elk at that distance under hunting conditions and keeping the bullet in the vitals), then it is unlikely that rechambering a round will have any significant impact. If you are shooting 1,000 yard elk from a prone position or other similar high-accuracy styles of hunting, then you are in a different definition of accuracy and I wouldn't do anything that might change any variable from my benchrest shooting, and that includes cycling a bullet through the gun multiple times.
Another important factor is bolt versus semi-auto (ignoring lever, pump, and other actions as they are much less common). Bolt guns are gentler on the rounds and often the round is guided into the chamber with very little contact with the throat of the barrel. On magazine fed semi-autos, the bullet feed ramps can mar the bullet a little, especially because releasing the bolt into the bullet is a much more forceful action and the feed ramps are designed for ensuring cycling under a wide variety of conditions. Here, multiple chamberings can have an effect on the bullet quickly.
I use a .300 Win Mag Nemo Omen like this one, and have to cycle the rounds in when I am out hunting.
My practice is to keep that same one round rechambering each time I go out, but the other rounds in the magazine I leave pristine. If I take a quick snap shot with the round in the magazine, it is because the elk are close (<300 yards) and the round's problems are probably not going to drive me out of that 18 inch circle of vitals. If it is farther out to where I have time and need to make a more precise shot, I will eject that top round. This has the added advantage of chambering the round just like I do in benchrest conditions. I let the charging handle fly free to seat the round, then I am going to immediately fire it. It hasn't been bumping along all day where minute changes of pressure on the bolt might change how the round sits in the throat of the barrel.
One thing I do to help preserve the surface of the bullet as it enters the throat of the barrel is to hand-load the round rather than let it be stripped from the magazine. The round can also be damaged when the ejector throws it out, especially if you are shooting plastic tipped (ballistic tipped) bullets as the plastic is really easy to damage. This makes the top round loaded in a way that doesn't duplicate my benchrest technique, but that top round is for shorter shots anyway.
It turns out that repeatedly chambering a round should be avoided, not because of accuracy, but for safety reasons. When a bullet is repeatedly chambered, it can cause what is called set-back where the bullet is pushed further and further into the brass case. This can cause higher pressures than the gun is designed for and that is dangerous. The type of firearm and round play a role in how likely this is.
I am not sure what the safe number of rechamberings is, as the problem is most often seen by people who do it often, like police and people who conceal carry. However, I would prefer not to find out, so it seems like a good idea to either rotate the ammo or use it for target practice at the end of the season.
