Thanks for your input guys.
(Nick Gammon) "... how about using a CR2032 lithium button battery...".
I would rather not have two types of battery to maintain for the system to work if there is a way to harness the solar panel.
(Nick Gammon) "Does this matter anyway?"
Come to think of it, the cycling reboots don't really matter(I hadn't considered that). But still, I suppose I'm just a stickler for the perfect solution. It feels like a cludge if the micro is repetitively booting up and crashing out on low voltage.
(dc42) "Why not use a 78L05 or other 5V low dropout regulator instead?"
I have tried linear and switch mode regulators with test solar setups and they work fine with full sunlight but when the voltage is getting marginal they tend to get unstable and some of them oscillate the voltage to the load. The zenner setup is simple and delivers a stable output voltage irrespective of the input voltage. For less than 2ma (probably much less) required to power the 85, it seems more than adequate and more stable.
(dc42) "... how about putting a large capacitor across the 5V supply?
I have tried this but it only slows down the cycling a bit.
(dc42) "Use the internal 1.1V or 2.56V reference instead of using the 5V supply as the reference."
Sounds good! Thanks. It will not give much granularity, converting the the 0-24 volts to 0-2.56 volts through a voltage divider, but it should be enough for my needs.
(cjdelphi) "... I'd have an analog circuit, using a voltage divider, that way when the voltage rises high enough (depending on the 2 resistor values), the base of your transistor will switch on"
This concept sounds good but if I could simplify it a little...
I could use the 85's brownout setting to prevent the micro starting up until it got over 4.1 volts. However a voltage divider would be connected to the reset pin of the 85, holding it low, so that the approximate 1 volt reset threshold would not be met until the solar panel was delivering, say, 12 volts. Enough voltage headroom so that the minor current draw, when the micro started, would not drop the voltage into unstable territory.
Does this sound OK?