If you have a call forwarding set up, it is likely to cause conflicts with voicemail. To turn off Call Forwarding or make sure it is not enabled:
Go and click the Start button on the recording tool few seconds prior playing your voicemail. When you are done, simply hit Stop to stop the recording.

"Dear [Prospect's Name], this is [Your Name]. On [Date of Last Contact], I contacted you about [Reason for Previous Call] and as I haven’t heard from you, I can only assume you're either, one, not interested and I’m simply clogging up your voicemail with annoying spam messages; or, two, you desperately want to contact me, but you’re trapped under a fallen filing cabinet and can’t reach your phone. Please let me know which one it is. I'll gladly send help if it's the latter. Just call me back at [Your Phone Number]. Thanks for your time!"
Android phones are made by a variety of different manufacturers, so saving voicemails differs slightly depending on the model you own. But there are some general steps you can follow to save those important messages.