ZME controller described an airspace infraction when a timely point out to ZTL was not accomplished; the reporter noting the supervisors staffing of D-Sides was late and ineffectual.

Narrative

I was working 2 low altitude sectors with multiple frequencies and also trying to assist the controllers around me as we managed the arrivals into Memphis. Weather was impacting all of us and the complexity of my situation increased fairly quickly. I eventually was over tasked and did not point out Air Carrier X to ZTL BHM Low. I knew the aircraft would be close to their boundary and planned to make the point but got busy with other duties. When I went to switch the aircraft to ZTL DAL Low; I realized that Air Carrier X was closer than 2.5 miles from the BHM Low boundary. It was too late to make the point out so I made sure that no other aircraft were impacted and then switched the aircraft to DAL. Recommendation; supervisors need to de-combine sectors during busy sessions and evaluate complexity. Staffing should be to the level that these sectors are kept open but they are often combined. Staffing is not adequate at this time to keep these sectors open during the day when needed. Supervisors should be required to staff D-sides and/or de-combine sectors without asking the controller if they think it needs to be done. They often take a reactive approach rather than being pro active. This point out I missed must be accomplished by every aircraft that departs HSV and is headed east to ATL. The flying time is less than 5 minutes from the ZME/ZTL boundary. This coordination could be alleviated by an AIT or changing the HSV LOA. Can we change the LOA to have these departures on a heading/routing that keeps them north of this boundary? Also; we often have to call ATL Controllers several times for coordination because of their workload. More often than not ATL Controllers must be called several times before we can accomplish this Point Out. This is a problem on every sector in Area 6 that interfaces with ATL.