Marriott Rewards points currently do not expire. However, the MR Terms and Conditions include language to the effect that Marriott can change the terms of the program at any time, so there's nothing to say they couldn't impose such a change in the future. I hope that's helpful for you.
According to the MR Terms and Conditions: An account may be closed at Marriott's discretion if no points are accrued during a 24-month period. All points in the account will be forfeited at that time. You may want to consider getting the MR Visa card and charge a few dollars on it every now and then.