I tested two different solar panels from garden lights. Both produce 2.60V in sunlight with no load and both conduct when dark. They even conduct a little in darkness with the 0.2VDC from my multimeter Ohms test.
That is why all solar garden lights have a diode to prevent the battery from discharging into the solar panel at night.
After three weeks of testing I get following results with this setup:
1. 9V 2W solar panel
2. 5x AA 1.2V NiMH batteries (Eneloop 1900mAh)
3. microcontroller and ancillary circuitry, 400 msec active @35mA, 15 minutes inactive (sleep) @0.050mA after a 5V LDO regulator (LM1117)
4. 1A Schottky diode between solar panel and batteries
The batteries charge to about 7.3V during daytime, the box containing the electronics and batteries gets to about 40°C, at night slow discharge from full load to about 6.5V in the morning with an inverse power distribution (as you have with capacitor discharge).
My conclusions:
1. a protection diode is necessary to protect the solar panel and prevent reverse discharge through the panel, and only looses about 0.4V forward
2. the 5V LM1117 needs about 5,8 to 6V to function, the 5 batteries even when partially discharged still provide more than 1.1V each, and when fully charged give about 7.2V total
3. the 9V solar panel gives about 9V in full sunlight, unloaded; connected to the batteries the charging voltage never goes higher then 7.3 to 7.4V. In morning daylight without sun the panel charges at about 7V.
4. given the extreme low current consumption of the load I believe that the difference in voltage between charged and half empty batteries is enough to keep everything running at night and allow the panel to fully charge the batteries in daytime.
This is just a little project but a nice learning tool for future use in larger consumers.
Edit: by the way audioguru, this project is using your fantastic moisture measurement oscillator circuit from several years ago.