Yes, a credit card issuer can close your account. Some reasons for closing an account include: inactivity (unless there is an annual fee on the card, the issuer only makes money if you use it); increased risk (in other words, the bank thinks you might default); and a general effort to shrink the bank’s credit card portfolio.
You can avoid closure due to inactivity by using your card occasionally and then paying the bill in full.
In many cases, the card issuer doesn’t have to notify you that your account will be closed. In cases where notification is required (such as when the closure is based on information in your credit report), the notice might be a letter that arrives only after your card has been rejected during a transaction.
Signing up for text alerts may help you receive and take notice of important information about your account sooner than by mail.