If you are getting 'decent power' with leaving your engine running, then the split charge relay is working.
Fully charge the battery with a battery charger as see if the battery holds a charge. What amp hour battery is it? Is it a leisure or ordinary car battery? How old are they? Most leisure batteries and some car batteries have a magic eye indicator. If your battery has one, what does it read?
There a dozens of threads on here about the limitations of split charge relays.