Good luck! You have encountered the very problem that gives this hub a bad reputation.

The left side cone adjustment, IIRC, requires 15 and 17 mm cone wrenches, and in my experience can either alleviate or exacerbate the problem.

Possibly your shift cable is getting caught somewhere when you fold/unfold, in which case it will not shift correctly until reseated properly. I used to have this problem before I shortened the cable housing as much as possible.

When you upshift (1 to 2, etc.) you pull against the internal spring, so in my experience upshifts are more reliable than downshifts (2 to 1). If you have trouble finding a gear in a downshift, such as can't find gear 4 when shifting from 5, it may help to shift all the way to 3 and then up to 4. Sadly, by the time you do that, you may need 3, or even 2.

For the same reason, shifting in the lower range seems to be more reliable than the upper range; I would often find gears 7 and 8 unreliable even though the others were fine.

A few months ago my hub got so bad I took it to a very good bike shop for overhaul. It had some 5500 miles on it. The head mechanic there has been working on Sturmey Archer hubs for over 30 years. Carefully following Sturmey Archer's published instructions for disassembly, he ... well, okay, he completely destroyed my hub. And so for the cost of the labor involved, he replaced the whole rear wheel with the newer version of the hub (XRF8-w). Now, with about 400 miles on the new hub so far, I have still had no problems at all. The jury is still out; but I'm thinking the new hub is really better.