I tried logging in both last night and this morning for 2 different family member accounts and was not successful. When I clicked on "Need Help Logging In" got a similar error message as chuck1 above:
This portion of the Southwest Airlines website is undergoing maintenance and is currently unavailable. Please try again later. We apologize for any inconvenience this may cause. If this issue persists, please contact a Southwest Airlines Customer Representative for assistance at 1-800-I-FLY-SWA (1-800-435-9792).