Firefox 81 on Windows 10
Processing Nodes are being shown as offline even though they are available. Even refresh does not change the status.

Clicking on each node results in showing the correct status.

Nodes should always display correct status.
Not sure how to replicate.
The nodes are refreshed every 30 seconds (or as you found out, if you visit the node's page).
Do the nodes come back online after 30 seconds?
If not, you might have run out of memory and the worker process in charge of refreshing the node statuses has been likely terminated, preventing the refresh to happen.
How can I observe refreshing of nodes? I think the worker process might have gone down. How to bring it back up?
Press the "Retry" button when creating a task (from your screenshot).
Shows the same error and the node status is not refreshed.
If not, you might have run out of memory and the worker process in charge of refreshing the node statuses has been likely terminated, preventing the refresh to happen.
Does not look like I'm low on memory. This is diagnostic for the WebODM instance. I'm running ClusterODM and NodeODM on separate instances.

Try:
./webodm.sh restart
?
It's possible that the worker gets killed when you process a task.
Tried this, seems good till now
Most helpful comment
Tried this, seems good till now