I sent you a detailed reply moments after your question was posted, I will send again, or you can scroll up to see it:
Unfortunately, the short answer here is no, this cannot be done, at least not in any practical terms. I know this may be disappointing to hear and that the lost message may be very important to you.
There is no mechanism for retrieving a deleted message, you cannot restore them yourself. Once they are deleted, the messages are, for all intents and purposes, gone. These machines are very basic, and don't have a "recycle bin" that can be accessed like your computer does.
If it was recent and no new messages have overwritten it, you have a better chance of recovery though. To do so, you'd need to take the machine in to a data recovery specialist. There are often local shops, with names like Data Doctors, they specialize in retrieving lost information from computer hard drives, memory cards, etc. They may be able to pull something off, if the messages haven't been overwritten, though the process is time consuming (often many weeks), and expensive (several hundred $), and would require dismantling the machine to the point it couldn't be used again. In theory, if they could extract the files, they'd copy them to a CD for you for long term storage.
So overall, while this is a remote possibility, the probability is high that you'll never be able to get these back. I apologize for being the bearer of bad news here, unfortunately there is no other practical way around this, these machines simply aren't designed for long term archival and don't make any accommodations at all for un-deleting, which I've confirmed previously with engineers at all the major phone system manufacturers, as this is a common problem.
Also, while you may not be able to get these messages back, a suggestion I'd make for the future is to switch from an answering machine to a voicemail service through your phone/cable company. Especially in cases of digital phone service, you can often access and archive your messages online, which would allow you to save any important messages to your computer or a disc, to ensure their long term preservation.
If you are prepared to spend $500+ to have the memory extracted, I can recommend some firms that may be able to take this case on, just let me know.
My apologies for the news.
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