I think immortal is the wrong word here. All organisms die. If it's not aging, then decease and predators will do it.
Biological immortality means after some point mortality rates don't increase with age - you can still grow old, it just won't directly kill you. Biologically immortal organisms don't have a max lifespan, if they're lucky they can just keep on going, but they may be dramatically more feeble than their younger counterparts.