Electronic – How to turn off DC-DC step-up converter to run on 3 AA batteries

I started this as a comment but the diagram was needed and you asked for critique as part of the answer

1. Place a ban on Olin coming within 10 miles of your diagram or he will kill you/it.

2. Your circuit diagram has much unnecessary non-functional mess on it that makes it much harder to read than is necessary. There are little marks and annotations everywhere that have no meaning to most readers and no place on a diagram that is meant for others to inspect for circuit design analysis purposes.

Consider this extract. Most messy stuff is marked. R25 value is very hard to read/ Large circles at component ends are very detrimental to appearance. Dot where vertical line from C3 meets grounds is OK and others should be like that or disabled for presentation purpises. It is fine for a drawing to look like this when you are working with it as long as it is not allowed to escape from captivity.

Depletion mode FETs have their place but it is very uncommon to need them and you should try hard not to do so. They are relatively old tech in most cases and have poor specs (as you found). As you note, a P Channel FET will do what you want about as well in most cases and biasing an N Channel on at all times as its default setting via a whisper of gate drive is acceptable if needed.

A boost converter may never have Vin > Vout + 1 diode drop unless you are happy for Vin to flow to Vout via the output diode. You may be.

If you rely on a processor to terminate a LiPo charge cycle, when the uC crashes the battery will too in due course.

Using a regulator's inbuilt current limit as a max chg regulator for a LiPo is OK only if allowable max I is >> Ireg max as reg max I out varies widely.
1A charge - what size cells?

More can be said.
Olin may choose to say some of it. Flame suits on :-).

First of all, thank you for specifying exactly which MOSFET you are using. It would also be very helpful to have a diagram showing exactly how you connected the MOSFET. Full schematic of the system from end-to-end would be best. I know you think you have described the circuit clearly, but the language you used is ambiguous, and I am forced to re-read several times, and then make assumptions.

I also think you might as well just explain why you would use one battery to charge another of the exact same type. Of course I can think of some possible reasons why you would do this, but since it is such an odd thing to do, I think you should explain it. If the setup you describe above is not your end goal system (that is, if you are systematically working your way up to develop some other type of system, you should explain what that is, too). For example, if you eventually want to replace the first battery and boost converter with a solar panel, then the whole thing is at least somewhat logical. But don't make us guess. Otherwise you will get all kinds of suggestions for more efficient ways to do what you are currently doing (maybe you could get rid of the boost and charge control and just make a simple current limited boost-mode DC-DC converter with no voltage output control or charge control, since it is impossible to over-charge the battery, assuming the discharged battery is at 20 or 30% capacity when you start).

I think there are three likely explanations for why things are not working as you expect. The first possibility is that you have wired the MOSFET incorrectly. A schematic and/or a picture of the test setup might help determine if this is the case.

Another likely explanation is that the MOSFET on resistance is large enough to foil the whole thing. The MOSFET you chose has Rds(on) specified as 250 mOhm typical at Vgs = -4.5V. But you only have, at best, 4.2V available to turn it on (if I understand correctly). So it might even be a bit higher. That may be a bit too high for the boost converter to work correctly.

Another possible explanation is that the battery being charged is nearly full. So the low current you see is just a result of low demand from the charger.

I can't think of any other explanations at the moment. The basic plan of putting a power MOSFET between the first battery and the boost converter is perfectly sound. The input bypass capacitor for the regulator should be between the MOSFET and the regulator.

Good luck! If you figure it out, be sure to come back and post an update.