If my recollection of Quantum Leap history is correct, we've seen 3 failed retrievals. And none of them sounded like "beeping".
The first time was in the pilot "
Genesis", and at the time there was no actual leap effect sound (or visual for that matter), other than the clock spinning back and the camera flying back and then upwards). At this point, leaps were depicted with dramatic orchestral music heavy on woodwinds.
The second time was also in season one with
Double Identity, where the project's efforts to retrieve Sam instead leaped him from
Frankie LaPalma into
Geno Fescotti, with the standard leap sound. I've edited together somee different leap sounds from season 1 to produce a representative effect. I have attached it below as a 192kbps mp3.
The third time was
The Leap Back, and for this one there is a unique variation -- a "mangling" or distressing of the standard leap sound. Again, I've attached this below as a 192kbps mp3.
For reference, I have also included a definitive leap effect sound that represents the seasons 2-5 leap effect.
I hope you find this helpful. If you need either of these as 24/96 WAV please let me know.