Thanks Jeff. I had you in mind, as you are using the only other 4-channel Ugly I know of to record similar material and you'd mentioned having similar issues. Glad you found this thread.
With my older V1 pair of 2-channel Uglies, I'd typically run 2 x DPA 4060 through each, recording to either two separate R-09s (early on) or to one DR2d. I never experienced overload problems using the 9.6V NiMH in those preamps in that way. I did a few times when using questionable alkalines early on before moving to the 9.6V NiMH batteries. I recharged the 9.6V Maha/Imdedion NiMh batteries after each use - typically after a run time of ~3hrs or so. However on occasion I'd run them for ~12hrs without problems at festivals. I'm not sure what their ultimate runtime was since I never test-ran them all the way down, but I remember estimating it at 20 - 24hrs early on and figuring I'd stay safe by always limiting my use to 12hrs or less. So given that, a general guess would be to halve those times for the 4-channel version, giving about 6 safe hours and perhaps somewhat more.
I have the same usage pattern for this 4-channel Ugly version, running all 4 DPA 4060s through it. As mentioned I've only used alkalines in it for the past 15 months that I've had this preamp. I've only noticed the problem with some really energetic low bass organ notes last winter. Since then I have not properly bench tested or otherwise tried to replicate the problem outside of normal use, and fortunately I've not had the same problem occur, but I suspect that is simply situational.
Since you've noted similar issues using the EBL Li-Ions and the same or very similar mic>preamp>recorder combination, I think I'll abandon this Li-Ion idea and replace the Maha 9.6V NiMH batteries instead. Once I do, I'll do a run-time test and try to remember to report back. I'll also let you know if I experience any overload with higher SPL bass heavy material.
If this does not remedy the problem, I'll consult with Chris. Perhaps I'll have him modify the preamp or do so myself to use two batteries in parallel or something, and have wanted to relocate the battery tray/clip from the side of the preamp to the end anyway.