Given that J-D has a +EV for the investor, you can expect every moment to be at least as sensible to invest than the next.
(Someone tell me if this is pretzel logic.)
Investment seems to go up when the site is winning and down when it's losing. Maybe that effect will reduce over time as people realise that the site really is going to profit the expected 1% in the long run and so get less panicked by large bets.
Given that betting volume doesn't go down when the site is losing, but total investment does, that seems like a good time to invest.