I can't remember the voltage range for the 5U, but if you're setting your Tekkeon's at the low end of the range, I'd suggest using the voltage more towards the high end of the range. That's how I run my VMS's to make sure that I don't go below the lower voltage limit in case the batteries sag at all.
Might want to get your meter out and check voltage the tekkeons are giving you when the vms switches over. Alternatively, the meter on the front of the unit is also a volt meter, so check to make sure your voltage is staying well up in the green zone the whole time before it switches over. If it dips down towards the red zone before it switches over it's an indication that your external battery is your issue.
Finally, though highly unlikely they're loose, go under the battery cover and make sure the fuses are securely seated. I suppose in some theoretical way, the fuse in the external circuit could lose continuity when the VMS warms up.