When do you give up?

It depends.
What is meant by not grouping?
Not putting all the rounds in one hole?
The rounds aren't all touching?
They aren't staying in the X ring?
An occasional flyer?
Scattered all over the paper?
You were probably not expecting a multiple choice quiz.
 
As they used to say in NASA, time for a system check.
1. Are you firing from a secure rest ?
2. Have you allowed another shooter of proven ability fire the rifle ?
3. Have you slugged the bore ?
4. How many different brands of ammo have you tried ?
5. Have you checked the stock to action fit ?
6. Have you checked the action screws tension ?
 
Your glass. Whether you bought it new, it came with the rifle, or carried it from another gun, it's possible that the thing is behaving like it was dropped on it's head.

Maybe lapping. I sure hope you won't sucker someone else with it to get it off of your hands. You should try savage customer support. They may replace the barrel and tune it a little.

You really have to check your expectations. You aren't going to get world class shooting from it.
 
Most rifles shoot a heck of a lot better than we do. What is it grouping now? keep in mind it's a factory rifle.
 
At this point, my best suggestion would be to find another shooter(preferably of known capability) to fire a couple of groups.
My older Son has intermittent spells of "the yips". The result is occasional loss of confidence in his scope and/or rifle. Having me shoot a few rounds assures him it's not a hardware problem and then I try to "re-align his software" and the problem goes away.
I've found rifles that were very finicky about their ammo so having a narrow selection of ammo makes finding that choice difficult or impossible. In this case, if the problem is verified by a 2nd or 3rd shooter, the piece needs to go back for attention. If the factory can prove it's accurate with a specific type/brand of ammo, at least the ammo cost of testing isn't on your dime
 
Barrel break in is usually completely unnecessary. Despite what Precision Shooting Magazine thinks.
Like g.willikers says, what do you mean by a group? Any .17 Hornet is a hunting rifle, not a target rifle.
You reloading? The .17 Hornet only come from Hornady. Your rifle may just dislike factory ammo.
 
What rifle are we talking about and what optics and mounts are you using? What bullet weights have you tried and what is the twist rate of your rifle? What position and what type of rests are you shooting from?
 
"The .17 Hornet only come from Hornady. Your rifle may just dislike factory ammo."

I see a conflict in logic in this comment. If there is only one source of factory ammo, shouldn't the rifle be capable of shooting that ammo satisfactorily? Shouldn't a buyer expect his rifle to provide adequate accuracy with the only available ammo?
Yes, I know that different rifles may "prefer" different ammo but when there's only one choice, the rifle needs to work with that choice. So far, the OP hasn't specified the level of accuracy he found nor what he expected.
 
A lot of good advice already.
What distance are you shooting at and how windy has it been on the days you're shooting?
 
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