You never said which vehilce you have, BUT...
Isuzu radio's do not ground through the wiring harness as you would expect, they ground strickly through the chassis.
If you aren't mounting the radio solid, you are just losing your ground connection.


1995 Trooper LS auto 3.2 DOHC /w SOHC intake
1989 Trooper 2.6 auto
1989 I-Mark RS DOHC 1.6
1991 Stylus XS DOHC 1.8