Thank god finally someone with the same problem, I've trawled the internet and you're the only other one I found! I'm in the UK on the carrier EE. My signal literally disappears and almost refreshes. Was every 5 minutes or so when I received the phone now it's ever 30 seconds. If you open the settings screen - the 'Carrier' option disappears for me whenever it drops out. Then if you try and make a call whilst it's dropped it says there is no SIM Card. And for the record I live in a 5 bar signal area (the antenna is on the building next door in fact).
I reset network settings, restored the phone, tried sim in old iPhone 5 (running ios8 so not a software issues), there was no problem. Tried a different SIM in my iPhone 6 and the problem was still there. Have contacted apple and this has been escalated to Tier 3 engineers. Waiting for a response (should be today) but I suspect it's a hardware issue that is going to require a replacement (and a 100 miles round trip to an apple store as I don't have a CC)
Disappointing but ultimately this happens with new products. Just want my nice new phone as I loved the 2 hours of fun I had with it