An Alternative Approach
Most answers here focus on teaching, generations and degeneration from an earlier state. I'd like to turn these, all be it fascinating and functional, concepts on the head. The deeper issue most answers touch on is teaching. Teaching and even the concept of civilisation are at their roots about the accretion, discovery and optimization of memetic ideas. Memetic ideas are rather abstract in human civilisation and are transmitted via the many flavors of teaching between generations. What if ideas take a more physical "hardware" form?
Enter Turritopsis dohrnii, the Immortal Jellyfish.
Like most other hydrozoans, T. dohrnii begin their life as tiny, free-swimming larvae known as planulae. As a planula settles down, it gives rise to a colony of polyps that are attached to the sea-floor. All the polyps and jellyfish arising from a single planula are genetically identical clones. The polyps form into an extensively branched form, which is not commonly seen in most jellyfish. Jellyfish, also known as medusae, then bud off these polyps and continue their life in a free-swimming form, eventually becoming sexually mature. When sexually mature they have been known to prey on other jellyfish species at a rapid pace. If a T. dohrnii jellyfish is exposed to environmental stress or physical assault, or is sick or old, it can revert to the polyp stage, forming a new polyp colony. It does this through the cell development process of transdifferentiation, which alters the differentiated state of the cells and transforms them into new types of cells. - Wikipedia
The key thing to understand here is that Turritopsis Dohrnii reverts to an earlier stage, beginning its life cycle anew. This is an example of intergenerational data transfer. True, Turritopsis Dohrnii only transmits genetic information, but what if it were more complex and could genetically alter some special sequences of its genome? Everything a member of this species knows gets not only saved in long term memory, but also in a genetic data storage organ.
As soon as a member of your species dies or is hurt badly, it commits suicide. The data from the genetic storage organ is then mixed with the seeds the dying one turns into. This might offer a really interesting reproductive cycle and has fascinating social implications. The species might be entirely asexuell or hermaphroditic, though an aproch to sexual reproduction is also conceivable.
If it is asexuell it might be a quite solitary species of lone geniuses, somewhat like the Jaghut from the Malazan series. They might live in symbiosis with viruses to use horizontal gene transfer to compete with or even outcompete the adaptability of sexual reproduction. They will probably have a very alien sense of self, as their memories have lived through a thousand bodies. Apperence and physical attributes might matter very little to them and concepts like childhood and age would be utterly alien to them.
If they are hermaphrodites or sexual, they'll most likely just exchange sperm packs like octopuses do and be done with it. Even the idea of relationships and marriage would be utterly rediculess to them, given that they would have a very long view of the world and would perceive all partnerships as necessarily temporary.
So, here are my ideas. I hope that you find them useful as what I'm suggesting might be a bit more alien than you bargained for.
PS: One could argue that this species isn't short lived at all but biologically immortal. This depends on what information is passed down the next generation. This could range from just factual knowledge, a database and nothing more, to biological mind uploading. Depending on where they are on this scale, they are either short lived of effectively immortal.