Hello!! Please help me with this one: my low E string gets flat and flatter as I fret up the neck. The intonation is perfect. What the heck is going on??

Are you fretting right behind the fretwire? If not make sure you are.

Other than that, check your intonation again. Don't rely on a tuner to measure it, you can be a lot more accurate with your ear if you concentrate. You don't get needle wobble with your ear either.
I strongly doubt it's a fret placement issue. You'd hear it on every string

EDIT
It could also just be a bad string. Very rare but does happen.

It's strange. It's only happening on the low E and a bit on the A. All the other strings are fine. Or maybe a bit sharp if I pull too much.

Yeah mate that sounds like either intonation or the bass side of the bridge has slipped forwards.
I'd guess intonation, you'd see if the bridge had moved forwards.
Spend a bit of time checking the 12th fret harmonic to the fretted note by ear. Forget the tuner, their nowhere near accurate enough unless you've shelled out megadough on a strobe tuner with accuracy to the 10'th of a cent. (theres 100 cents in a semitone)
You can do far better by ear if you simply concentrate. Turn all the gain and effects off, roll your tone pot to zero. That will stop your ear getting confused by extra harmonic content.

Pickups set too high?

Arjay

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Good call.

Yup, lowered the pups. Better but still a bit flat. The saddle itself is maxed all the way back. Where should that be? It seems like it could be anywhere to start. Tune it and then set the intonation. This is a 2008 American Deluxe

Sounds like the bridge has moved forward, common on Deluxes. It's the knife edge of the tremplate on the bass side. It wears down fast on some, on others it lasts forever.
I've exactly the same problem on my 04Deluxe.
You can just see on this photo. By comparing the leading edge of the tremplate to the nearest edge of the pickguard, the two are not parallel.



Other than taking the saddle off, removing the spring and then putting the saddle back on. Your only other option is to mill down the back edge of the saddle, or get a new tremplate.
A thicker gauge string on that low E can sort it, but causes extra tension at the trem, so you end up with the same problem again at a later time.

Two thing come to mind....

1) Is the neck strait in the pocket?

2) Have the tremolo pins come loose?
That intonation it all wrong.

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At first all you want are Hearts and Diamonds.

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Okay a picture is worth a thousand words here.

The tremolo is either worn out in the bass side knife edge or the tremolo stud has shifted in the body.

_________________
Marriage is like playing cards...

At first all you want are Hearts and Diamonds.

But in the end, all you really want is a Club and a Spade.

Sight unseen, I would venture to guess that your neck has too much of a bow.

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You dig?

maybe I should take it to someone. Messing with the neck in the pocket and the truss rod scares me to death. I've wanted to try the neck flat though, with no relief. I don't see any obvious sign of the bridge moving forward (thanks for the picture) it looks perfect. I don't remember bonking the neck to shift it in the pocket, but I'm sure I could have.

You'd have to have that neck in a very severe angle for it to reduce string length enough to affect intonation. Same with neck bow.
Yet we often see Deluxe owners on site with the bridge problem.
Now I know that bridge plate doesn't look severe enough to warrant all that saddle movement, but it's all it can be. I've been over that guitar with a fine toothcomb. To the point of lazer lining through the center of the neck dots then checking the posts are both on the same 90 degree line from that line.

It's one trait that doesn't seem to pass on to the American Standard trems. I'd like to see whether there is a significant saddle length difference between the polished saddles of the deluxe and the milled saddles of the Standard. That could explain a lot of it.

I've had the same problem with a Yamaha Pacifica. I had put on a larger set of strings and couldn't get the E and A strings intonated correctly. Come to find out the pickups were to close and the heavier strings had more magnetic pull and would put it out of tune. It seemed fine without fretting a note but as soon as you worked up the neck the closer the strings got to the pickups and the problems started. Cheers

Hey, thank you, thank you for all the great ideas! If it drives me crazy enough, I'll just swap out the Deluxe saddles for the other type. How would I set them though? 25 1/2 inches for the high E and the rest also?