The second half of this compound adjective is usually pronounced with a short i (livved), as if it were derived from the verb to live (rhyming with give). However, short-lived derives not from the past tense of the verb to live but from the noun life (which has a long i). Just as a dog with short hair is short-haired—derived from the noun hair (there is no verb to hair!)—or as a person with a big heart is big-hearted—derived from the noun heart (there is no verb to heart), something with a short life is, technically, short-lifed.
Now, it is important to recognize that f and v are, respectively, the unvoiced and voiced versions of the same sound: an f is essentially a whispered v (whisper the word very and it sounds like ferry). So it is a simple change—replacing the f with a v, but retaining the long i vowel—from short-lifed to short-lived, correctly pronounced short-lyved.
Consider also that one blessed with a special gift (a noun) is not gave or even given, but gifted. (This is also another example of the f-v conversion.)
This mispronunciation, the erroneous change from short-lyved to short-livved, is irrational and should be resisted. Perhaps this solecism will be short-lived.