Therefore I would power the 85 from the 12v solar panel that can put out up to 24 volts. The zenner/resistor network would regulate the voltage to the 85. I was thinking a 4.3v zenner.
Why not use a 78L05 or other 5V low dropout regulator instead? It's more efficient than a resistor and zener.
However I have a couple of problems related to hysterisis that I need resolved. As the sun comes up there will be weak power from the solar panel. The voltage may be just enough to power the 85 into an unstable state but not enough to fire it up properly. To overcome this I would set the brown-out on the 85 to 4.1 volts. I would use powersaving settings on the 85 and would expect a current draw of, say, < 2ma. But still I am concerned that the solar panel will just get up enough voltage to exceed the 85 brownout; the 85 will power up and exceed the current available from the panel; the voltage will drop; brownout occur; 85 drops out; voltage rises... and so on. How do I get around this?
If you run the 85 at a low frequency, you can probably get the current consumption well under 2mA. If the situation you describe occurs, why not put a delay at the start of your program, so that you know the power has remained stable for some time before it does anything?
If you are worried that when you start the charge pump, the voltage will drop, how about putting a large capacitor across the 5V supply? That will power the 85 long enough for it to detect the drop in solar cell voltage and stop the charge pump.
Also the 85 is measuring the voltage of the solar panel through a resistor divider connected to one of its AI pins.
This voltage will be measured relative to the supply voltage to the 85 (or that applied to AREF but the AREF pin doubles as MOSI which I use to communcate with the charge controller). Therefore, when the solar panel is providing just a few volts at the start and end of the day (and below the zenner voltage), the voltage reading (as seen by the ADC) will be incorrectly overstated and the 85 will tell the charging chip to pump current into the LiPo when it shouldn't be.
Any views on how I can fix this?
Use the internal 1.1V or 2.56V reference instead of using the 5V supply as the reference.