Right, kept sealed it will still make good beer. But if it takes up some moisture, weights could be off leading to inconsistencies. Not necessarily enough to account for the entirety of the OP’s variation, but one variable that could be eliminated. And if not kept well sealed, I don’t think Briess gives any such assurances. I wonder how much variation he’s seeing between batches made identically – malt milled on the same time schedule in the same way, at the shop or at home – as opposed to across all of his brews. Raw materials may not be exactly what the software assumes. Or I may be after another red herring.
Maybe I’m blowing it a bit out of proportion.
Here’s the bh efficiency from some of my most recent batches:
67.3% (last time I brewed this it was 73.6% when milled twice)
65.8% (expectedly low due to bigger grain bill)
72.6%
70.5%
69.3% (last time I brewed this it was 73.6%)
68.4% (last time I brewed this it was 66.3%)
70.4%
65.7%
Over about 100 batches I average 71.1% brewhouse and 74.3% mash efficiency which isn’t horrible. I’m obviously more concerned about the inconsistency that is anywhere from 65%-79% for average OG beers. It makes designing a new recipe a nightmare. I basically have to use my average efficiency and keep my fingers crossed…
I hear you. Consistency is something you want, because predictability is so important. It would drive me nuts. And that range of variability is not insignificant as I see it. When you’re always running the same system, you’d expect a new malt you’ve never tried to be the one uncertainty, and hope to dial it in with one brew. Got to be an answer.
You guys probably have something with grain crush consistency. I’m brewing this weekend and will try to add pictures. Time to save up for a better grain mill…
Well when you’re ready I have an unequivocal endorsement I can make. 
Hey I’ll take it now and file it away!!
Monster MM2 Pro, with the 2 inch rollers. I recently upgraded to this and am thrilled to have the only one I’ll ever need. The larger diameter rollers give a far superior crush to any 1.5 inch jobs. You don’t need three rollers, just 2 good ones!
Are you using flaked oats or other flaked adjuncts? I’ve noticed my efficiency to drop inconsistently when using flaked oats enough so that the next time I use 'em I will probably boil them before adding to the mash. I’ve tried grinding them without success.
Another thought: are you getting dough balls? I’m guessing not, but doesn;t hurt to ask.
Another issue seems to be that you don’t always have a good estimate of mash efficiency. In my signature line, is a link to an efficiency calculator that I tweaked for estimating efficiency of batch sparging.
Flaked grains sometimes. I have the extract potential set super low in Beersmith as I notice a dip as well. Some software has the the extract potential for flaked set to the same as base grain which has not been my experience.
No dough balls. I make sure to stir well and destroy any at mash in.
I plan 70% BH efficiency and usually get 1% on either side. Occasionally, I get 2% plus or minus but that’s acceptable in my brewery which I attribute to an agricultural product and amateur brewer. I see you have a cpl brews outside my personal tolerance which would bug me, too. I surely hope you find the culprit.