I'm suprised they're shutting down because of a lack of a buyer/investor rather than making it and keeping it as a successful business. Are the goals these days for a big buy out?
Bandcamp was similarly private for 15 years after taking a few rounds of funding, but they eventually got acquired, and I guarantee you that's because those investors pushed for an exit while the projected future revenues of the company justified a higher valuation.
I myself worked for a company that was private for 12 years after seed funding and five rounds of VC capital. But eventually we were pushed into a (poorly conceived) acquisition.
The merry-go-round always stops. It's just a matter of time.