Yes, your fiancé visa does expire.
Once your K-1 petition is approved, you will receive your fiancé visa from the U.S. Embassy or Consulate in your home country. Your fiancé visa will allow you to enter the United States immediately. If you need some time to get your life in order before moving permanently to the United States, just keep in mind that your fiancé visa is only valid for up to 6 months after it is issued. You must be prepared to enter the U.S. on your fiancé visa before those 6 months are up.
Upon arrival to the United States, you must marry within 90 days or your fiancé visa will no longer be any good. This deadline is not extendable and if you are not married within the 90 days, you must leave the United States.
The United States Citizenship and Immigration Services (USCIS) approved your fiancé petition and issued you a fiancé visa because they believed you and your fiancé were serious about getting married. Therefore, they give you just enough time to come to the United States, plan your wedding, and get married. It may sound like a lot to do in such a short amount of time, but it is definitely manageable. Many other couples have done it and so can you and your fiancé.
If, however, you do not get married before your fiancé visa expires, you must leave the United States immediately. Failure to leave the United States will subject you to some serious consequences, including potential denial of other immigration benefits. If you manage to stay in the United States for more than 6 months after the expiration of your fiancé visa and you are still not married, you may even be barred from the United States for up to 3 to 10 years.