Your Odyssey might be on the way out? It should be able to supply higher Pulse Cranking Amps than a normal wet cell battery (ie. PCA= cranking current measured for 5 seconds, CCA's are rated for a longer period - 30 seconds IIRC?)
However an AGM (absorbed glass matt) battery like the Odyssey should recharge a lot faster than your stock wet cell type. I've got a different brand of AGM in my RSC and it is very quick to charge up (using a 10 Amp battery charger) compared to my other two vehicle's which have normal wet cell batteries. So, with your engine running it shouldn't take long for it to fully charge.
Perhaps charge your Odyssey fully and then take it to a battery place the following day and ask them to test it?