I've hunted ground hogs for almost 50 years now and I've always used bolt action rifles with magazines. BUT...
In my opinion you don't give up much if anything with a single shot rifle. The important consideration here is accuracy and having a field shooting aid that will provide you with the maximum chance to hit the vitals at the distances you choose to shoot.
In my early days, if I missed I tried to take a second shot and invariable I missed again or worse wounded the hog because I rushed the shot. What I learned is most of the time you are better served if you miss the first shot to take you time for a follow up shot. Often a short pause to reset yourself and let the hog calm down works better for me. Therefore a single shot rifle works just as well as a repeater.
If the miss was low and kicked up debris in front of the hog chances are you won't see him the rest of the day especially if it's late afternoon. If you missed high, chances are you'll get another shot opportunity. Sometimes they don't even spook if the high shot goes into the brush. Even if they spook, often they will come out again if you wait and they were just starting their feeding cycle. Therefore the single shot rifle doesn't give up much if anything.
For this reason, I sight in all my ghog rifles to shoot a little high. Three possible outcomes: 1. you make a lethal shot - all is good, 2. you miss but don't spook the hog and get a second shot, 3. you miss but spooked the hog and because the shot was high he may come back out since you didn't rattle him too much. Again the single shot rifle works as well as the repeater in this situation.
With low shots the reverse is often true, i.e. you gut shoot the hog and he makes to his hole and is doomed him to a slow death or you kick up debris in front of him, scare the s*** out of him and won't see him the rest of the evening. Rushing a second shot can have the same ill effects.
Bottom Line: I rarely have situation where a repeater has an advantage over a single shot rifle. Not because I'm a great shot and always make a first shot kill but because trying to rush a second shot often results in a miss or worse, a wound. Also I like the "one shot - one kill" mentality. Have I made second shots - yea but it's the exception rather than the rule.