How to stop iphone deleting contacts

Are you syncing contacts from different devices? Are you using iCloud to do so?

Did you already try to reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again? You will not lose any data by resetting, but it can cure some glitches.

If this does not help, and to rule out a software issue, setting it up as new device would be the next step:

How to erase your iOS device and then set it up as a new device or restore it from backups