On my iphone 4, I added 2-3 contacts manually in the contacts list. After some time when I try to call them, they do not appear. When I enter manually the number it is displayed in the phone number preview on the keypad. How is this possible?
That is possible if you have them in another contacts list or location
Since they are still on your phone, when they show up using the dial pad please look what list/location is it.
Maybe you should follow the instructions when adding new contact.
Assuming you do not use any kind of synchronization. (iCloud ect..)
Make sure you are looking at all groups, and they are not is SIM only.