Yes, trade routes are regularly recalculated at the beginning of each turn and I checked the city screens after these updates. But I didn't check for blockades during peace vs. blockades during war. I did now and it's true: the city loses all trade routes if you are not at war and blockade with a privateer (well you cannot blockade with anything else during peace). That's when one of your privateers collects the blockade gold (only 1 unit per city!). The city's isPlundered flag is set to true and no trade routes are calculated, even if there are possible trade network connections like in the above example.
If you are at war (like I was with Izzy) the privateers won't collect gold and the city's isPlundered flag remains false (it's always reset to false in the IBT), so that possible trade routes will be calculated for the city.
The availability of resources is purely depending on the integrity of the trade networks, so even if a city loses all trade routes in times of peace due to being plundered, it will still remain access to all resources via the remaining/intact trade network paths.