I guess I'll just summarize the commentary. I don't expect this to be an answer, just what I see from the discussion.
I'm imagining something like the following image.
There are some spikes in the required current, which last \$250\:\text{ms}\$. The required current peaks at around \$75\:\text{mA}\$ and then falls back to some other current level (sleeping) for approximately \$10\:\text{s}\$, though this period is variable. Every \$45\:\text{s}\$, the battery is removed (no clue, at all, as to why -- it's all just magic to me) for about \$30\:\text{s}\$. So the total cycle time is \$75\:\text{s}\$.
The goal is to minimize the average power to help maximize the length of service for a battery system, before replacement.
From the above, I would also assume the following:
- No services are being provided while the system is sleeping. So it would be still better if no power was consumed in between. In other words, the only useful periods are the ones that are occasional and consume \$75\:\text{mA}\$ for \$250\:\text{ms}\$.
Because of the length of time for the active period being \$250\:\text{ms}\$, I feel it's just fine to continue the idea of using a PIC MCU. The complaint I might otherwise have, were the period much shorter, would be that it takes a while to get a PIC MCU started from a "cold" sleep -- the oscillator just takes time to get up to speed. On the other hand, an MSP430 can fire up to full speed in about \$1\:\mu\text{s}\$. But given the duration, the MSP430 advantages mostly disappear. So that makes me quite comfortable with the PIC MCU approach here.
As I gather things, you need about \$20\:\text{mC}\$ of charge during the active period of time. The PIC MCU has a range of voltages over which it operates, and similar things can be said about whatever else is attached. Let's say that the allowances you can accept are a droop of no more than \$200\:\text{mV}\$ during the active period. Ignoring contributions by the battery, and putting the entire burden onto a capacitor, this means a capacitor value of \$100\:\text{mF}\$. With a low voltage type, it doesn't have to be that expensive or large. And this assumes that the battery itself can't contribute during this time (which it probably can.)
The average current required is less than \$2\:\text{mA}\$, given your statement of about \$10\:\text{s}\$ between activation events. This can be provided by something as little as a CR2032 lithium battery (which is not known for high currents.) Perhaps placing a capacitor in parallel with such a battery, with a current limiting resistor of course, would provide the necessary power supply without the need, cost, complexity, and/or quiescent losses of a voltage regulator.
Of course, you have other issues to deal with and I have only a very narrow tube-like perspective on your project. But what you've written so far takes me towards that kind of consideration as an alternative path.
The approach I'd like to have you consider would be to arrange things to use a capacitor as your reserve storage, add a current limit arrangement to the circuit so that the CR2032 battery isn't hit hard when first charging the capacitor, and just go with that. The PIC MCU can go into a decent sleep with fairly low draw. End of story.
