Is liberal democracy facing an existential threat(s)?

[TJ in Oregon]

Not really. The populist wave that's been taking place has still been within the bounds of liberal democracy, apart from countries that weren't really sold on liberal democracy in the first place (Russia, Turkey, etc.). It's not like 2016 has been filled with coups overthrowing elected governments.

There are a couple serious threats still that may lead to existential crises in the future if continue. The first is that peoples' faith in "the system" is dependent on the perception that the system is actually defending their interests, jobs, security, families, values, etc. If, whether due to social change, economic transition, or some other sort of unsettling factor, people no longer see "the system" as working for them but as being asked to work for "the system", then confidence in "the system" will be shaken from top to bottom.

The second is that those who view themselves as liberal democracy's most fervent defenders forget its premises in the silencing of their enemies. When decisions begin being made by mobs instead of at ballot boxes, countries can start a spiral toward mutual escalation. When "fascism" is simply whatever collection of views the beholder disagrees with, a loss of civility follows. People would prefer finding their concerns met by acceptable options, but if their concerns are washed out from the acceptable options, they will ultimately find other options who are willing to listen.