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Yes, they can. Miles will expire when an account becomes inactive for a period of three months or more. An inactive account is the one that has no miles credited to it during three months. If you keep earning miles, do not violate program's terms and keep your account in good standing, your miles should not expire.
However, you can avoid such problems altogether, if you get a general travel card that doesn't ever let your miles expire. There are plenty of such cards, they are usually applicable for most airlines, meaning that you can put your Spirit purchases on such a card and earn miles and also use earned miles for Spirit. If you want some help with choosing the card, the we can even give you some advice on a particular one. The one that clearly stands out is the Discover it® Miles. The reason is that it offers rich rewards while not requiring you to pay extra.
The rewards program is 1.5 miles on all purchases which are matched at the end of the first year (provided you are a new cardmember) - an analogue of a sign-up bonus, only it depends on you. But since Spirit gives a very modest sign-up bonus of 15,000 miles, with Discover you'll earn more anyway. Obviously, miles never expire. And the cherry on top is that there's no annual fee.