We might be able to slow, stop, or even reverse the aging process at some point, but that would not make a person truly immortal. If we could end aging then people could become "ageless" and remain at the same biological age; so in effect someone could stay 28 years old for their entire life, but their body would be no different from a 28 year old right now, meaning that an ageless person would still need to eat, they could get diseases, die from accidents, etc.

To achieve what you are describing would require technology that is WELL outside our capabilities, and even if we had some sort of rapid automated body repair systems those would still have limitations. However, if we become sufficiently clever to achieve the sort of immortality that you describe, then chances are we'd include an "off" switch.