We really need to know what caliber and cartridge the rifle is, manufacture of ammunition (Remington, Federal, Winchester, ect.), grain and type of bullet. Good shooting!!

Yes, this is quite common! This is the reason why you can' t just zero in at 25 yards, and then go hunting and expect to hit anything at greater ranges! A very small error at short range is magnified significantly when you move out to greater distances!! Shooting at 25 or 50 yards is good for " getting on paper" at 100 or more, but the final zeroing has to be done at ranges of 100 or more yards, the longer the better. I only have access to 200 yards now, so that' s the range I use for confirmation of hunting zero! I wish I had 400 yards.

No, after getting on paper at 50 yards, move to the 100 yard bench and finish your zeroing there. I recommend you sight your ' 06 in to hit +3" @ 100. It will still be about the same +3" @ 200, and about -5" or so at 300, and this should allow a dead-center hold on a deer' s rib cage out to 280 yards and kill' em!! If you have access to a 200-yard target, after getting it +3" @ 100, fire a couple more at 200 to verify where it' s shooting at that distance!

I don' t know what grain bullet you' re shooting but my guess would be 150-165grn range because thats what the majority shoot in the 30.06 and also velocity is going to play a role in sighting in too. Have you ever chronographed your load? I shoot a Hornady 130grn Spire point in my 30.06 and i' m sighted in as follows....+3" at 100yds, +1" at 200yds,0 at 250yds,-5-6" at 300yds.

Toons,
All bullets start dropping the second they leave the barrel.
To match the line of sight from the scope the barrel has to be tilted upward to create an arc for the bullet flight.
Each load will have two zero' s. The first one will be at close range like 25 yards where the bullet passes through the line of sight of the scope and will stay above the line of sight of the scope out to roughly 250 yards where it will be at zero again, after that the bullet falls below scope line of sight again and stays there.

From a 25 yard sight in groups will be 4 times bigger at 100 yards roughly.
A 1/2 group at 25 yards could be a 2" group at 100 yards.
After getting close at 25 yards you really have to shoot at 100 yards to sight in your rifle. If you have the space then shoot it at 300 yards and you will be able to figure your trajectory for all points in between and you can get your 400 yard drop figures from a chart. If you know the velocity from a chronograph it helps but with your 100 yard sight in, lets say 3" high, and your 300 yard drop amount, lets say 3" , you can get a pretty good guess at your velocity from the drop chart.

Depending on where you are hunting is how you should sight in your rifle.
For open country where long shots my be required a 250 or 300 yard sight in is ideal. For areas where shorter shots will be the norm then a 150 or 200 yard sight in would probably be better.