The Elamites were around a long time, and changed their writing system. Probably the old one was good enough at the time, but like most early inventions, was found wanting after a while.
Lost Languages:['Civ commented] Amusingly, the author reproduces a letter to The Economist magazine regarding its article on the Phaistos Disk. The letter calls it a century old fraud (the disk, not the magazine) that could be exposed as such using thermoluminescence. [p 298]. [/snip]
The Enigma Of The World's
Undeciphered Scripts
by Andrew Robinson
I refreshed my memory a bit. Linear Elamite {linear? Linear B [??] confusing enough} and Proto-Elamite. Apparently affected by Akkadian.
***the Phaistos Disk. The letter calls it a century old fraud***
The Phaistos Disk is questionable. I think the thermoluminescence testing would help.