so here's what it looks like with the command line

nafa@NAFABox:~$ /usr/bin/indiserver -v indi_weatherradio
2021-01-18T22:28:22: startup: /usr/bin/indiserver -v indi_weatherradio
2021-01-18T22:28:22: Driver indi_weatherradio: pid=3666 rfd=3 wfd=6 efd=7
2021-01-18T22:28:22: listening to port 7624 on fd 4
2021-01-18T22:28:22: Driver indi_weatherradio: snooping on GPS Simulator.GEOGRAPHIC_COORD

does it help you understand my problem?

Not yet, since this only shows that it is working. You should log the output so that we can find the problem.
/usr/bin/indiserver -v indi_weatherradio >> /tmp/indiserver.log

I think it lasts about 7 days. Is there a way to make it reboot automatically every hour at a certain time?

I wouldn‘t recommend it, better track down the problem. I have it running for months without a problem.

PS: And something out of the question, since you're so good, would it be possible to get a statistic of the nights?
so that we can know which nights were good during the year.

I‘m not so sure what you mean. Is this more than the recording done for the weather radio web page? Take a look at my own instance here: