I too have had this problem, notes vanishing on my iPhone 4. My observations are:
1. This is not a Mountain Lion problem. I have Snow Leopard on my MBP.
2. This is not an iCloud problem. I don't use iCloud.
3. This is not a Google problem. I do have a Google account but it is in no way linked to my phone. I have a Yahoo mail account linked to my phone.
4. I never had a problem with vanishing notes until upgrading to iOS 6 and its updates.
Hence, like others have said I believe this is a STUPID APP problem đ ..This is not like Apple to have such an inferior product! Stupid problems like this was the biggest reason I made the big switch from "Windoze"/Android to Apple a few years ago.
Fortunately my notes have never vanished from my Yahoo mail (syncs automatically).. The work around I have found is to email the missing notes to myself (from the MacBook since the "notes" folder isn't visible on phone email) and then copy/paste back into notes. But this is getting a little OLD, this is about the 5th or 6th time I've had to do this in the past couple of months. I've got better things to do with my time!
This is the last straw, I am putting my foot down and switching to a different note taking app, or as the OP said resort to old-school method of carrying a pen and real notepad around in my pocket. It wasn't that hard in the past, and I've never lost a real notepad out of my pocket.
đ BOOO to you Apple! Wake up and fix notes please!!!