My response would be on the same lines as BenW and Vargmatll. Check to make sure the barrel is free floated and that everything that is suppose to be tight, is tight. Maybe have a competent gunsmith go through the rifle to make sure everything 'specs' out.
As for the .308, it is probably the most inherently accurate .30 caliber cartridge ever developed according to many reloading manuals. The military loads their M118 White Box(173gr.) and M852 'Mexican Match' (168gr.) to 2,550 fps at 70'+- from the barrel. Those loads were/are suppose to shoot sub MOA and were kind of the de-Facto test round. If a rifle didn't shoot that load especially M852 it was time to check other variables.
The test target I received from Remington with my .308 rifle, that had a 24" barrel, measured .49" Avg. and the load was 37 grains of 3031 behind a 168 grain "Match Bullet" ignited by a Remington 9 1/2 primer.
A suggestion would be to get yourself a reloading press such as an RCBS 'Rockchucker' or the like and start to reload. In my set up I started with RCBS dies then switched to Forester FLS BR dies and never looked back. Not touting one over the other, just do some research and buy what trips your trigger.
I have had twist rates of 1 in 12", 11" and 10" and barrel lengths from 24" to just under 26" and would be hard pressed to say any of them didn't shoot well.
As for bullet weights I have shot a wide range from as light as 130 grain up to and including 200 grain. The 130's were loaded to about 2,800 fps and shot sub MOA groups in the .50" and less range. As for the 200's they were loaded to about 2,200 fps and shot a tad larger than .65" groups.
If you have a Chrome Moly barrel you should get 4,000 rounds through it before you will see a gradual decline in accuracy especially at the 600 yard and beyond ranges. As for SS barrels they usually see a more pronounced drop off in accuracy at around the 5,500 -5,700 mark and that was about the time I would plan to re-barrel my rifle(s).
Keep experimenting and good luck.