That is extremely weird.
I have a couple of questions and a suggestion:
Do these 6 people whose text messages get deleted have anything in common between each other? For example, are they all on a certain carrier (like AT&T or Sprint) or a certain type of carrier (All GSM), or do they all have Droids or iPhones.
Also, when you first bought this new phone, did you get a new number? I ask this because a little while ago I had a similar problem and it ended up being that the prefix 337 (the first 3 numbers of my new number) was not recognized as a cell phone by other carriers so the text messages would get to me and be instantly deleted because their phones thought they were texting a landline instead. I fixed that issue by having to change my number unfortunately.
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Suggestion:
It obviously sounds like something is being restored when u use the DM onto the device that's causing this issue. The only thing I could think of is to use BlackBerry Protect (go to BlackBerry Protect on your device to download it if it's not already on your device) to back up certain parts of your device. In the Options menu in BlackBerry Protect select to back up everything but Text Messages.
Once that's done, wipe the device completely and test out that the random deleting text message problem is gone like when you first got the second device from your carrier.
If the problem doesn't present itself after a complete wipe, use BlackBerry Protect to restore your address book and other info. Hopefully a setting doesn't transfer over using Protect that might transfer over if you used the DM instead.