Is it possible for you to lose your taste buds?

Not really, however: Well short of placing your tongue against a belt sander, taste buds don't actually get lost, but may atrophy or lose/diminish the ability to taste for a number of different reasons. Some medications can alter taste sensation. People who smoke generally can't taste as well as non-smokers. Without the sense of smell taste is a bit limited. This is why people with colds can't taste very well.

Yes: Most people do not actually loose their taste buds, they just loose the ability to taste. This can be temporary due to medication or an illness or it can be more permanent. Check out the medication you are using such as asthma inhalants, etc. On the web to look for side effects and then contact your md to ask about specific medications.

No: But with age our taste buds do get de sensitized, and people say they are lost. Young children, for example, rarely apply hot sauce to foods, but many adults use it routinely.