> I'm using a precision reference (Analog Devices REF191) an a classic
three
> pin regulator constant current source configuration
> i.e. Vout is tied to the floating ground pin via a current setting
> resistor, and the load is connected to the floating ground pin.
> In this case, the regulator forces 2.048 volts across a 2.1K ohm resistor
> (Rset), giving me a nominal 1.01 mA constant current output.  This
circuit
> can be found on most three pin regulator data sheets and cook-books.

Are you sure that your regulator's maximum current draw is under 1 mA?  One
problem with the constant current configuration you're using is that the
regulator's operating current can't be any higher than the load current. 
Common LM317-ish regulators can't be used as a constant current source
under about 10 mA for this reason.

One solution that has occurred to me is to use two regulators - perhaps 10
mA in parallel with the load, and 11 mA in series with them.  I haven't
done the math, but I suspect that there may be a very limited load
resistance range that will keep both regulators within their operating
voltage ranges.

Or you can use a constant-current diode, which are available down into the
microamp range.  Unfortunately, they're hard to find, ridiculously
expensive from the few sources I've been able to find, and aren't all that
accurate.
        Jason Harper