Rebloom means a plant blooms a first set of scapes, rests for a period of time after it has finished blooming, and then sends up another set of scapes.
Recurrent means that before the first set of scapes is finished, new scapes will appear. Because few people understand the term "recurrent", hybridizers have started using different terms such as "instant rebloom" or "continuous bloom".
Extended bloom has nothing to do with rebloom...that is a term that describes how a flower will partially open the day before and remain open for a longer period of time.
While many people blame the hybridizer when a plant fails to rebloom or perform the same in their garden it is, as Julie said, usually lack of appropriate watering that is causing the issue. Daylilies need a LOT of water to look their best and rebloom. Rebloom scapes often have a different scape height and bud count than the original scapes.
