Elvis faked his own death in 1977 but has died since.
"Elvis sightings" were a fairly common occurrence in tabloid journalism from the late '70s through the mid/late '90s, but when's the last time you read of one in the checkout line?
Gladys Horton's parents, or possibly the mailman himself disapprove of the interracial relationship and so they've been intercepting Elvis' letters and sending them back.
Elvis' faked death was intentionally presented as tabloid fodder with just enough misinformation thrown in to make people think it was simply tabloid fodder.
Elvis had to disappear for some reason in 1977 (witness protection, poor health, exhaustion, etc.), and his close confidants knew that someone would eventually leak info about the hoax for monetary purposes, so they beat the would-be leak to the punch by leaking it themselves
in the best way they could to make the whole idea seem ridiculous. It wouldn't be the first time that reverse psychology was used to affect popular opinion.
Elvis isn't dead but in hiding.
Tiring of all the attention, Elvis faked his death and is living in his home town of Tupelo, Mississippi, in a secret bunker under the Tupelo Airport.
His death wasn't actually a hoax. Like many liches, however, it was part of a Thanatos Gambit
to restore his popularity. Elivs sightings are because either being lichified stop the rate of decay, or he has expert prosthetics. The latter explains why nobody has been able to conserve his presence.