PS. I don't think I've ever had a Gibson that stayed in tune for several songs:)
Mike
I've never owned an actual Gibson but I do like the LP shape / design / sound. For this reason, I have a PRS Stripped '58 and a Tokai LS165 Goldtop with a pair of P90's. Both were cheaper than US made Gibsons (in the case of the Tokai, by a big margin), both are wonderfully finished and both stay in tune for several days with a set of 10's on them. Well, obviously depends how you hit them but seriously - I can put either of them down after playing for an hour, go away with work for a week, pick them up. And they surprise me if they're NOT in tune. Sure they drift if the weather changed substantially but otherwise? They'll be pretty much where I left them..... If you've got a great guitar with strings that are new-ish (i.e. stretched in but still good) then IMO your tuning shouldn't be giving you so much hassle.
Whilst I agree with others opinions here about getting the nut looked at, I did have one guitar which was woeful with tuning no matter what. It was a Chinese made Eastwood that was an old Mosrite clone. I bought it unseen and got my fingers burnt. This isn't me complaining about all Chinese guitars / Far East builds because I've got a couple of G&L Tributes and a Burny - all are great guitars for the price paid. The Eastwood did indeed go out of tune during songs. I can do setups to an extent but I'm no professional and it was beyond me. I had a new nut put on it and a full set up from a guy I trust locally that has set up other guitars perfectly. It beat him too. The neck profile changed with the wind and consequently so did the playability and, of course, the tuning would go out. That was a naughty guitar that no longer lives here. I hope that with your guitar it's just the nut that needs sorting and, for an expensive US made guitar, that's likely to be the case 
Good luck whatever you decide
