[Updated - see pictures below]
I treat joinery in the UK for rot by drilling 10mm holes, injecting fungicide gel, and hammering home a tapered cross-grain oak plug to seal the hole. I've been using exterior-grade PVA smeared on the inside of the hole to fix the plug. After hammering home, I immediately plane the plug flat, while the joint should still be open. After 24 hours, I apply a conventional exterior paint finish.
Revisiting a property I treated 6 years ago, I see that about 25% of the oak plugs have moved enough to crack the paint finish. Not one plug has come loose, but some have moved enough to crack the paint, and that is unsightly, and will let in water. I'd like to fix the plugs more reliably to avoid this. The glue has to work in the UK, which can be hot, wet or freezing.
I asked Loctite if they could recommend anything. They said they weren't sure anything they had would be better than PVA. I need an easy-to-use glue, since I insert thousands of these plugs, often working at height outdoors on old buildings. It's hard to experiment, since all the plugs look great for a long time after the painting. I'd prefer to have just one visit for glue-and-plane-flat, without having to wait for the glue to cure.
What glue can I use? Or what better plugging process can I use?
Update two days later, following great suggestions from answer and comments:
Here is a close-up picture of paint cracking at oak plugs in 2016. These are oak plugs hammered into an oak frame and glued with with pva in 2010. The frame was made about 1939. Actually what species of oak was used for plugs or frame is not known. The paint is Dulux weathershield Exterior high gloss over Dulux weathershield undercoat (I think this was just after the shift from old-style high-VOC paint to low-VOC paint, and before the takeover by AzkoNobel, but I may be mistaken).
Looking closely, I can't see any evidence there that the plugs have moved out of the holes. It is, as others have suggested, paint cracking at the boundary between the woods, despite the fact that the grain is aligned and the woods are vaguely the same. So my plea for better glue is not useful.
I found it hard to take photos of plugs that haven't cracked because they're so hard to see! Here's just one:
I have a suspicion that the reason that did not crack is there may be a smear of epoxy over it. That plug is oak in softwood. The softwood had major rot, and I filled a big hole nearby with Repair Care Dry Fix and Dry Flex 4-pack epoxy. That sticks very strongly to wood and flexes with it, and a smear might well stop the cracking.
@bowlturner suggested that different woods might be to blame. I did start off long ago trying to match plug wood to frame wood, despite having to custom-make all the plugs. But I gave up because the softwood plugs tended to break up as they were hammered in. They need to be pretty strong to stand up to the insertion process, especially halfway up a building in a gale. It may well be true that oak in softwood tends to crack paint more than oak in oak. But oak in oak does crack too.
@Graphus suggests filler. The only filler I have found that does not crack with time (and I hope that means decades) is the Repair Care 4-pack system. That would probably work, but the setting time is such that the fungicide gel will probably leak out before I can get the hole filled. I would have to plug the hole and leave a gap at the surface to fill - I will think about that.
Much thanks to everyone for the ideas! Keep them coming if anyone has anything more. Meanwhile, I will tick the answer from Graphus because it contains much wisdom.