Reliable secondary storage for Raspberry Pi (or other such single-board computers (SBCs))?
The question is not clear about the volume of data to be stored. 


If the volume of data actually being written in each cycle is not very high, an USB flash memory device would be a good option: Low power requirement, low cost, and write/erase cycle ratings of 10,000 (consumer grade) to >100,000 (industrial / mil-spec) for multi-level-cell (MLC) flash.
A Flash-based SSD typically has the same endurance per MLC as an USB flash drive, but due to a greater amount of spare cell head-room, write optimization using on-board RAM buffers in some models, and better write leveling algorithms, is often rated for 1 million to 5 million write/erase cycles for the device.
Downside: More power required, 500 mA will often not cut it.
A RAM-based SSD with on-board back-up battery is an option if the application requires even higher write cycles. Very few manufacturers offer pure RAM-based SSDs any more, though that was the primary early SSD technology. Write cycles are essentially infinite in comparison to the above options.
Downside: Most RAM SSDs are not USB but PCI or PCIe, so an adapter is needed, as well as external power.
Finally, there is of course the conventional magnetic storage external hard drive with USB interface. Lowest cost per gigabyte, and very high write/erase cycles.
Downside: External power needed, and they are sensitive to physical shock.