I would first check your transmission fluid dipstick - pull out and wipe off on clean white rag or paper towel - then push all the way back down in and pull out again to check fluid level on the dipstick (usually has to be warm and in neutral/park when doing this - check manual, which will also tell how to read the dipstick). If low this can cause reluctant shifting. If dark colored (usually should be a thin cherry red, occasionally another color but always thin looking) or has black streaking on the rag, foaming, or is burnt smelling then your transmission needs professional help and flushing. If you need to add fluid, be sure to use recommended type, and should if at all possible be same brand as is in there now - different brands of lubricants or coolant do not always play nicely together.
Sometimes the shifter hydraulic valves just get out of adjustment or dirty or sticky or their springs break or get weak - commonly with ones that have gone way too long without fluid and filter change (yes, automatic transmissions almost always have filters - commonly the bottom cover plate has to come off to change it/them - some have 2).
Also, many types of transmissions have variable friction shift plates and/or bands or belts or discs that control the shifting and slip during shifting to keep it smooth and not jerky. On many or maybe most brands these have to be adjusted periodically (typically every 30-60,000 miles), which means (in most cases) taking the bottom cover plate off so best done along with a fluid and filter change.
Also - with most brands, the more load on it, the longer the transmission waits to shift because it assumes you want the higher torque for rapid acceleration during starting out from an intersection, entering a freeway, or passing - so if you accelearate aggressively the shift can wait quite a bit loner. Many cars you can get up to 30 or so in first, up to 45-60 in second for instance if you floor it when accelerating - and when driving, tromp on it and it will generally downshift if going less than about 50-60 too. This also happens more in small engined cars that high-power ones, because the engine is pulling harder to move the car.
