I think the best way to preserve the rain water
might be to seal it in full ziplock bags, without
any air. That's how to preserve opened bottles of
wine! Or, more precisely, one inflates a balloon
in the wine bottle to block the air.
Unbuffered solutions such as rainwater will not
keep a constant pH, which is why we buffer our
solutions if we want a constant pH. But I think
the rainwater pH will stay reasonably constant if
you store it in a container without air. I'll
recommend plastic - maybe a plastic storage box -
because I think glass might be more likely to have
reactive groups on its surface.