Sorry for the delay in response.
The good news is obviously that there doesn’t appear to be anything wrong with your hardware so long as you’re away from home.
One thing I’m not sure has been clarified on this issue: when you’re connected at home, do you have strong signal strength in all parts of your house? Or does the signal become unreliable as you move from room to room? I’m just wondering if the phone or tower thinks it has a handshake when it’s actually been lost, and is failing to reestablish when the signal strength goes back up.
I’d be surprised if you can’t just log in to your VM website account and access your entire detailed call history, which, depending on the carrier, will note the general location (but not which cell towers). If you see any calls from home while you were away, yes, that would confirm something is seriously compromised.
If detailed records are not immediately available on your account, I can only suggest you call your carrier and describe the issue in detail, including that you have no problem when away from home.
I strongly suggest you carefully write out a summary of the conditions and how you’ve tested against it, so you can repeat the exact same details clearly when they inevitably ask you over and over and over to describe the problem, during which time they are also going to drive you mad with the classic gems of restarting your phone, resetting network settings, resetting all settings, restoring the phone, etc.
They might, however, be willing to reset your account at their end, which I’ve had to do on occasion myself with Sprint, T-Mobile and AT&T; and apart from losing any stored voicemails (copy/export anything you want to save first), and having to reset my account PIN and voicemail greeting, it has solved any number of weird issues.
It’s not impossible that the caching at you local substation is involved, and such a reset will clear the node to more reliably connect to your device.
Another experiment you can try is to buy a cheap MMO pay-as-you-go SIM, and swap it out just to see if it is more reliable. It will be, of course, a new number, and any calls to your existing number wouldn’t ring through unless you first set it to forward to the test SIM; and outgoing calls would be from the new number and not recognized by your contacts; so keep that in mind. It’s a very effective way to challenge your carrier from the identical phone at the identical times and locations.
Let me know if this continues.