If the Duocharge is set up correctly, then the next two suspects are the house bank, followed by the charger. The DC will not send a charge current to the start bank unless the house bank is fully charged. So if it doesn't sense the house bank as being charged, it will never send a charge to the start bank.It does not "trickle charge" the start bank. This could be caused by the DC not being properly adjusted, or by a bad house bank or the charger. See the instructions here for ways to properly test the condition of the battery banks:
Trojan Battery Company