POI moves with same load ...

As has been said above, could be different climactic conditions. Light, wind speed and/or direction, humidity, barometric pressure. Potentially these could change enough during the course of a day to affect, let alone over a few weeks/months.
Particularly over a long enough time between sessions I might even suspect that the stock absorbing moisture could have an effect. Are all your guns by the same manufacturer and should be assumed to have the same kind/degree of stock sealing?
Shooting a few months apart brought the thought to me that is might even be an effect of wearing different type or thickness of clothing.
Unless your powder is poorly stored, I wouldn't suspect that too much initially. As for your patches deteriorating, maybe?

I think in a way you answered your own question as others have. you are dead certain everything is right and the same with the rifle and components, so that only leaves one thing, the shooter. shooting an open sight rifle can be tricky even for the best shooter to get consistent point of impact from session to session or even from shot to shot. and the further the distance the more chance for a different point of impact. if you are chaining your sight picture are canting your rifle or head in the least it will matter! if downward or upward pressure on the rifle is different from shot to shot it will matter! I am 63 and have been shooting since I could walk good and it has happened to me countless times, there is nothing mysterious or complex about it. in fact it is simple,,,,,,,,,,,,,,,,,,,,,

Last year my .54 shot about a 1 1/2" group at 100 yards, last time I shot it it would only print about a 3" group at 50 yards. My eyes have taken a down turn in the past year (cataracts) but I should be able to do better than that. Same load, same sandbags, I have been shooting this gun for at last 7 years, I don't remove the barrel for cleaning, this one has me stumped as well.

Eric.....You mention perhaps A vision change? Few years ago I did an experiment . I put a cheap and dirty bent sheet metal test peep sight on my long rifle , held on w/ the tang screw. The result was just what I needed. I could see both front and rear sights , and the target was visible , all three w/o a ball of fuzz around each. Went to the range and the result was my trusty old .50 once again shot as advertised.
I'm sure you aren't to this stage yet , but I figured , good time to build a shorter , lighter , rifle w/ no rear sight , and installed a custom made compact tang peep sight. I'm back in business , though the peep sight keeps me out of competitions. I'm a practice shooter , and still hunt ,so who cares about the formal stuff , anyway?..........oldwood

This happens to me all the time I will be dead on at 50 and 100 yards for about 6 or 7 shots and then i will start shooting 3 to 6 inches high or right it’s definitely me My eyes getting tired and moving my shooting position. When I first started shooting i was chasing my rifle until I realized it was me not the rifle or sights.

I made a tang mounted peep last year, I haven't given it a serious test run yet.

Without a peep I see two fuzzy rear sights, one on top of the other and just a fuzzy hint of the front blade.

I'm beginning to suspect the only thing that's consistent is inconsistency.

I find my old eyes fatigue after about half an hour of shooting and the sight picture becomes real hard to maintain. I often have a hard time deciding which of the two front sights to use as it blurs into two right next to each other.

Try this for blurry eyes. Put simple regular saline eye drops in your eyes before going to the range . This cleans the thicker mucous from eyes . Makes a huge difference in the amount of accurate shots I can get off , before fatigue sets in.
Learned this lesson the hard way. Was out w/a friend sighting in a copy of the classic Lion and Lamb rifle built for him. He couldn't sight the new rifle in due to an eye problem . It takes me about 10 to 15 shots , filing the front sight off to bring the shots up onto the center of the target. Around the 10th shot , my old eyes were so full of mucous , neither sight was viisible. Quit the sight-in process to come back another day. ..........oldwood

Fortunately I am not having an eye problem. I can see the sights clear and the target crisp. With the same sight hold my group has moved up about 3-inches at 100-yards. The 5-shots are still a good tight group, just higher than they were a few months ago. I found two of the 5 patches and they look okay but not as clean as I am used to. I think my 7:1 water/ballistol "dry" lube need refreshening. Usually I can smell a little odor from the lubed material and usually I can feed the slightest slickness (or oily). These seem mostly odorless and dry. The only other thing I can control is where the bag is under the fore stock. I can't recall if I had it between the wedges, on one or the other or somewhere else. The rifle is fully bedded, not disassembled for cleaning and the wedge pins are snugly in place with no sign of movement. Some change to humidity shouldn't effect it although a big change in humidity or temperature might. I noted that when the rifle was right on at 100-yards the temperature was 82 degrees and for these past two sessions it has been 88 and 92 respectively. I am going to try again with fresh patches and lube and I will move the front bag around to see if it makes a difference. This will all have to wait until I return from my bear hunt that starts tomorrow (using longbow for this hunt). Thanks for the suggestions!

Col. Batguano said:

Some times odd things just happen. One day the groups are in the center of the bull, and the next day they're way off. Since I pull the barrel each time I clean, once I suspect this is happening I pull the barrel and re-seat it. It's only happened a couple of times, but each time it's happened, re-seating has returned it to the bull center. It hasn't happened since the first few half-dozen or so times I shot the gun, so my suspicion is that it was the barrel just shooting its' way in to the barrel channel.

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The NMLRA has a very good book by the champions of each type of shooting regement.It's called Shooting and Winning with the Champions. For any type of BP shooting reading it is a good place to start. Lots of info to help you out with problems. NMLRA on the internet.

Lotsa factors can be involved. Change of hold due to wearing different clothes in changing weather. The stock can change due to changes in humidity. Are the barrel pins/keys tight? If so, not a good thing. They should be loose to allow wood movement without stressing the barrel.