If it’s the breather hole, then I think that the inner seal head (the gubbins in the box on the left of the picture) is probably leaking.
The valve / disc is just screwed into the bottom of the piston rod, so I suppose that joint could leak…
This video is quite good once you get used to the Bond villain accent – look about 1 minute in:
[video]https://youtu.be/-w0X0-AOhRA?t=47[/video]
Double check, but I think everything marked ‘6’ is in the basic service kit – so in theory, it should be sufficient to solve the air leak problem. You wouldn’t need to disturb the oil side to do this (as long as you don’t pull the piston rod out of the top half). However, since your post is spongy, there’s air in the oil side which could well pop the piston out of the top half (possibly violently) when you loosen the inner seal head (this is beyond what is shown in that video). There are ways to try and get around this, but they are not without risk. Unless you’re prepared to do a full rebuild, my vote would be to get a specialist to do it. (Or buy a new one :-/)