I don't have time to dig into it at the moment, but it should be possible to use similar techniques to e.g. eBay bidding software to open a page and send the appropriate button click. Whether it can be done with existing nodes or would need either a custom node or some JavaScript magic is also something to look into.
Based on the underlying protocols involved I can't see any reason why it shouldn't be possible.
For example, if you open Chrome on Raspberry Pi,
I have a page localhost:5000/mqttsettings.
On this page there is a button to save mqtt.
This is a function that automatically presses the mqtt save button when a specific message comes up.
The reason for doing this is to receive mqtt from the current nodered.
But strangely, I don't know why, but after a few hours the reception suddenly cuts off.
I do not know the cause, but if I reboot or press the save button of the mqtt setting page, it will resume again.
So, I asked how to press the save button as a way to do it without rebooting.
Which log did you check and what do you mean about there being only a star?
Exactly what stops?
I thought it was the sensor that stopped. Do you mean the node-red can't publish to MQTT? You must be more explicit about what happens, without knowing the details it is difficult to help.
Something else I don't understand. You said you connect to the sensor using localhost:5000, but that is a web page on the computer you are running on, not the sensor. So what software is providing that interface?
You will need to inspect the source for the page that provides the button to work out what it is doing when you click it. Hopefully it is just doing an http get or post of some sort, but will depend how or what security is in place as to whether you can just replicate that with an http request node.
If you want you can click a button from a Node-RED flow by using WDIO nodes. This will then force a dependency on having an instance of Selenium to execute the request (e.g. Selenium-Standalone) plus Java. It works but is a lot for a simple button click.
As stated previously: confirm what action the button does when clicked and approach it from that direction.
Might be as simple as a POST with certain parameters.