As Nighthawk points out, it is most likely a shooter problem. Lifting one's head to see the effect of the shot is probably the most common fault regardless of target type. We all want to see the hit and move our heads but regularly fail to remember that doing so leads to a miss.
Another common fault is incorrect foot positioning. One often shoots from whatever position they are in which may not be the most conducive to the shot. Another common problem is to set up for the shot initially seen rather the one actually taken. Just like with clays, look at the target presentation, determine you insertion and break points, and set up accordingly.
Lastly, misses could be a gun fit factor. If you are wearing more layers hunting than when shooting the gun may be a little long. I find this to be more of an issue in gun mount than fit as I do not get a good fit to the shoulder if I am the least flawed in my mounting technique. Working on proper gun mount with your hunting clothes would be good practice.
If all this fails, my next step would be an eye exam. It is not high on the list but it is something that should be done occasionally for a number of reasons besides shooting problems.
Shooting problems/slumps are rarely the result of equipment but it is more acceptable than blaming one's self. It is far easier to buy new gadgets than correct behavior not to mention more fun. Good technique with "poor" equipment will end up with better results than good equipment with poor technique. Rule out technique before working on equipment, one will find acceptable results sooner.
