Run threw the test on both relay's... and I myself would test the relay when it's acting up, normally when hot they give problems..
As for the bog you speak of, it could be a number of things, but Fuel pump, and fuel filter would be on my check-list..
Good rule of thumb on honda's I've noticed is if it don't prime and start on the first spin, then the pump is old and worn-out.. But that's me, replacement parts are to cheap just to over look.. Most pumps run 2-300K, but Oem don't last forever..LOL