What voicemail service are you using? Verizon's standard *86 Basic voicemail will let you recover deleted voicemails from the same session if you have not yet hung up. Once you hang up and decide a day or two later you need one back, it's too late.
Visual Voicemail has a trashcan and the voicemails can be recovered from the trash for a time,
Other services like YouMail and Google Voicemail may have a trashcan where deleted voicemails are stored and recoverable for a period of time.