What kind of solar panel is required to keep a mobile alive forever?
If you want NEVER run out of battery, you should come from ALWAYS extreme cloudy condition at shortest day, because weather statistics cannot guarantee cloudy time duration limits.

Note, solar battery manufacturer gives power output for very optimistic conditions, say clear day and battery oriented directly to sun.

Daylight wikipedia article gives you range of conditions you'd expect. According to it, in extreme cloudy day there's less than 0.002 of max. light intensity. Add here 40% daylight time. So you will need rated power of ~2000 times consumed to work forever (1 KW solar battery for 0.5 W device).

So you have to define less strict requirement to get reasonable values, say 10% per year failure rate. Then I expect about 10-20× solar power, say 5-10 W solar panel and larger accumulator (week of autonomous power). But accurate value require much statistical calculations or experiments.