Unstable connection to remote behind router with two ISPs; asymmetric connectivity

I have an appliance behind a customer network (which I don’t control).
I can ping it, but after a minute or three it will stop responding.
Then, after a similar amount of time, it will return.
This affects ssh and other traffic over ZT as well,
impacting diagnosis (and real work).

In the web console, I notice that the external IP of this device
alternates between two different IPs (which I’ve traced to different Internet providers), which I think is related to this issue.

What can I do to ameliorate this situation, or at least further diagnose/understand?

Some more info:
when I can’t ping remote from my machine, from a third host on our ZT network, I can.
And vice versa, but there is no correlation: e.g. there are also times when
we both can/not ping the remote–they seem completely independent.
But me and the third host never have connectivity issues between us.

[Note once logged in to remote via ZT, I ssh’d out creating an
ssh-tunnel to a non-ZT host, which then allows me a stable, ssh login
to remote not using the ZT network, and then verify this wasn’t basic connectivity issues.]

And then there’s a fourth ZT host in AWS (acting as VPC router) which
the remote can ping without (seemingly) ever having this periodic packet loss…

Thanks for any ideas.