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I've made three tests, spinning the phone and keeping it at different angles (moving it both slowly and faster in the process). It constantly vibrated throughout each test...
The only mention is that when I was quickly flipping the phone the vibration stopped for less than half-a-second (maybe even less). After that, it continued to vibrate strong and continous. I assume this is normal, since the motor was re-calibrating for the new position?
-later edit-
OK, I've been to the closest Vodafone center (the store from where I've actually bought the phone) and I've tried to reproduce the "issue" on another kit. Same behaviour, I've easily managed to follow all the steps mentioned above and kill the vibrations! So it's not a problem at all, most likely that's how the Z1 should act in that particular moment. Pfew! 
Try a RESET by pressing the Power + Volume UP key for 5 Seconds. If that doesn't helps visit your nearest Sony Service Centre.
My apologies for the double-post, it seems harder and harder to reproduce the "issue". Though, it did happen twice today after constantly spamming the letter/back/space buttons when writing a text message, again only by keeping the phone in a vertical position.
I tend to believe it's how the Z1 is built. I mean, vibrations work perfectly other than that. Can anyone else check this please? It would be much appreciated! 
I've tried recreating your issue and am not able to do so. I've held the phone in various positions, but to no avail.
Thanks SwitchTrix.
It seems I now have troubles reproducing it myself. I'm pretty sure it's how the Z1 is supposed to behave, not being an issue at all...
I mean, if the vibration system was faulty I guess it didn't matter in what position I was keeping the phone, plus the fact it was either randomly either it would have stopped completely.
Anyway, if anyone encounters this please let me know, I'm ore than curious to see the outcome.
-later edit-
Ok, I might have found an easier way to reproduce it without spamming or anything. While keeping the phone in your hands, in a vertial position - slowly move the right bottom corner towards you & the ground. Anyone? 
By the way, who knows where the vibration motor is located?
The vibration should not stop working when holding it in a certain position or angle. If it does i recommend that you contact a service location or local Sony Xperia support (http://www.sonymobile.com/global-en/support/contact-us/) for assistance.
When testing this, make sure that you're not tapping the same key repeatedly though. Alternate between at least two different keys.
Pressing just a single key might trigger this behaviour?