I am curious, does accuracy in a rifle deteriorate over time? Does something change with the rifle that just reduces it's accuracy?
You can wear out the barrel or damage the crown. It takes quite a while to wear out a barrel and most civilians will not ever see it happen.
There are several factors that limit the accuracy of our shooting.
1. Limitations of the weapon
2. Limitations of the Ammunition
3. Environmental Factors
4. Limitations of the shooter
Firearms have an inherent accuracy. For example, most infantry weapons are up to 8 MOA accurate with the average being ~2.5MOA.
A Minute of Angle is defined as 1 inch at 100 yards...2 Inches at 200 yards...3 inches at 300 yards so on and so forth.
So a 2.5 MOA weapon can only put a bullet in a 2.5 inch circle at 100 yards. That is as accurate as it can get.
Sniper weapons and high quality firearms designed for maximum accuracy can be as little as 1/4 MOA.
Ammunition also has an inherent accuracy defined in MOA. Variations in bullet weight, powder charge, and bullet design effect the accuracy. Match Ammunition for example has the lowest variation due to stricter quality control and is therefore more accurate. Bullet weight and barrel harmonics also combine to effect ammunition accuracy for individual weapon designs. For example, a G3 battle rifle tends to be more accurate with 150 grain bullet than it does 175 grain match because it was engineered to shoot the standard infantry ball ammunition. Weapons are engineered around a specific design ammunition. That does not mean you cannot shoot any ammunition of the same caliber, it just means when they did the math, the harmonics were optimized for specific forces and the closer your ammunition is to those forces...the more inherent accuracy to a point. That is why some "recipes" of bullet weight and charge are more accurate than others in a given firearm.
The environment affects accuracy. Temperature, humidity, and wind all affect the burn rate of the charge, peak pressure, flight time, and flight path of the bullet. Heat causes things to expand and cold to contract. A cold bore will have a different point of impact from a hot bore. Even target perspective can affect accuracy. Shooting uphill vs shooting downhill will change your zero. If you zero on a cold day then our zero will change on a hot day. It does not change much but it does change and the extremes require a sight adjustment. The biggest environmental effect is wind. Wind will push a bullet significantly off point of aim. Learning to read the wind and account for its effects on your bullets flight path is an essential skill for a long range shooter. It is a mark of skill.
The most important factor we can influence is the shooter. The fundamentals of shooting become very important and the shooters ability to apply them determines just how much of the inherent accuracy of our equipment we can squeeze out.
Breath control - shoot at the natural pause in your breathing cycle or at least when no air is moving in or out of your lungs. Breathing causes the rib cage to expand moving your firearm off the intended point of aim.
Relaxing - Do not muscle the weapon and shoot from a natural point of aim.
Aim - Proper sight picture and sight alignment. Front sight post in focus when the firearm discharges and follow thru establishing one shot with two sight pictures.
Squeeze - pretend the trigger is a button or a needle going straight thru your body that you must push thru it without any side movement. It doesn't matter where you place your finger on the trigger so long as when squeeze...it is straight back. Proper trigger control and reset skills.
So you can see that mastering all of this is both a fun and lifelong process! Most importantly, relax and have fun!