When you travel outside your home country & you have Data Roaming turned off, you will still be notified via Apple Visual Voicemail when you receive new voicemails.
If a phone rings once and then goes to voicemail or rings only briefly, it You can't definitively know the cause of a phone barely ringing and going to voicemail because neither a phone company nor the phone's operating system provider will tell you if your phone number is blocked.

Important note: In some states, such as California, it’s illegal to record calls or conversations without permission from all parties involved. If that’s the case, ask your call participants if it’s OK if you record the conversation before you start recording. Then, ask again once you do start recording—so you have their permission on record. Alternatively, if you state “I’m recording this call for [whatever purpose]” and your contact stays on the line, that’s OK as well.
Great question! Although I don’t know if there is a specific function for this on your particular phone, the best way to save the message is the simplest. Turn up the sound as high as you can and record it onto a digital recorder (like you would use for a lecture), a cassette recorder or your cell phone if you have a voice recorder on it. Then save it as an MP3 on to your computer for safe keeping. You can also Google your vtech model number to see if you can find an owner’s manual. They might have a way to save a recording in there. Probably not, but it’s worth a shot.