Electronic – Xbee series 2 drops off network without apparent cause – diagnostic suggestions

I've built a meter reader, based around an ATMega 328P and an XBee series 2. The initial protoype built with an Adafruit trinket pro (3.3V) and it worked like a charm. It was stable for 10ish days, before it ran out of battery.

To improve battery performance, I moved it to a breadboard-duino. This is where the problem starts. I start it with a newly charged battery back (4*1.5V hybrid NiMH) and it's fine for ~7ish days, as the battery pack voltage slowly drops from 5.7V down to ~5.1V. Some time around this point (and it varies by >0.1V) the XBee dissociates from the network. I know this because 1) Power cycling the xbee only restores connectivity 2) The XBee association LED activates, rather than blinking and 3) The 328P can be regularly seen trying to put the XBee to sleep.

However, if I restart the xbee (or entire circuit, ether way) the issue repeats itself – but in a timeframe of a day. This implies to me it's related somehow to the battery decay, as that's the only thing that doesn't get reset.

However:

• Power output is regulated to 3.3V by a TS2950CT 3.3V regulator
• Measured circuit voltage is 3.27V, nonfluctuating on my meter
• The trinket pro worked all the way down to a supply voltage of 3.6V
• There's a 100uF capacitor between the +3.3V and ground for smoothing
• After the blocking diode, supply voltage is still 4.69V
• Drop out voltage on the regulator is listed at 450mV, worst case, with a 100mA load. This is, at worst, half that.
• All the components are rated at 3V, except for…

The only dodgy thing I've done is (accidentally) used a 16Mhz ATMega. I've got an 8Mhz crystal in the post, and I'm going to replace that ASAP. But it's Christmas, and if I'm lucky it'll be here by new year.

So, what I'm asking people is – what else can I check? What could it be? Where could I start looking?

Oh, and, relevant seasonal greetings. They'll be merry if I can get this thing to work!