The BBC weather app is flakey I am afraid. You could try deleting the apps cache and see if that helps. I have changed to the excellent Transparent clock & weather app, free from the Play Store.
This app offers a myriad of settings and configurations and I am using it on cell tower location, (Use my location), only, as opposed to, "Use my GPS", location and find that it is remarkably accurate and very, very, battery friendly. IMHO, the best weather and clock app out there.